V KONFERENCJA METODA REPREZENTACYJNA W BADANIACH EKONOMICZNO-SPOŁECZNYCH PROGRAM I STRESZCZENIA

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1 V KONFERENCJA METODA REPREZENTACYJNA W BADANIACH EKONOMICZNO-SPOŁECZNYCH PROGRAM I STRESZCZENIA th CONFERENCE SURVEY SAMPLING IN ECONOMIC AND SOCIAL RESEARCH PROGRAMME AND ABSTRACTS

2 Organizatorzy Akademia Ekonomiczna w Katowicach Uniwersytet Łódzki Polskie Towarzystwo Statystyczne Komitet programowy Andrzej Barczak, Czesław Bracha, Czesław Domański (przewodniczący), Lorenzo Fattorini, Zdzisław Hellwig, Jan Kordos, Walenty Ostasiewicz, Jan Paradysz, Jan Steczkowski, Jacek Wesołowski, Janusz Wywiał Komitet organizacyjny Janusz Wywiał (przewodniczący), Józef Kolonko, Alicja Ganczarek, Wojciech Gamrot, Grzegorz Kończak, Tomasz Żądło (sekretarz). Cel konferencji W ostatnich latach obserwuje się wzrost zapotrzebowania na dane statystyczne uzyskiwane szybko i niskim kosztem. To określa rolę metody reprezentacyjnej i znaczenie konieczności rozwoju znanych procedur zarówno z praktycznego jak i teoretycznego punktu widzenia. Konferencja umożliwia zaprezentowanie ostatnich osiągnięć w tej i w pokrewnych dziedzinach i daje możliwość wymiany doświadczeń w zakresie praktycznych zastosowań metody reprezentacyjnej. Tematyka Estymacja parametrów populacji na podstawie danych z prób nieprostych Wnioskowanie na podstawie danych niekompletnych Statystyka małych obszarów Optymalizacja kosztów i liczebności prób w metodzie reprezentacyjnej Wnioskowanie statystyczne z wykorzystaniem informacji dodatkowych Podejście modelowe Badania wielookresowe Zastosowania praktyczne

3 Organizers The University of Economics in Katowice The University of Łódz Polish Statistical Association Scientific commitee Andrzej Barczak, Czesław Bracha, Czesław Domański (chair), Lorenzo Fattorini, Zdzisław Hellwig, Jan Kordos, Walenty Ostasiewicz, Jan Paradysz, Jan Steczkowski, Jacek Wesołowski, Janusz Wywiał Local organizing committee Janusz Wywiał (chair), Józef Kolonko, Alicja Ganczarek, Wojciech Gamrot, Grzegorz Kończak, Tomasz Żądło (secretary). The aim of the conference In recent years a growing need is observed for statistical data, collected quickly and at low cost. This defines the role of the survey sampling and the importance of improving survey sampling procedures from theoretical and practical perspective. The conference gives an opportunity to present latest developments in this and related fields and to exchange experience on practical applications of survey sampling. Conference topics Estimation of population parameters based on complex samples Statistical inference based on incomplete data Small area estimation Sample size and cost optimization in survey sampling Sampling designs Statistical inference using auxiliary information Model-based estimation Longitudinal surveys Practical applications of survey sampling

4 Monday 8 september Tuesday 9 september Wednesday 10 september Sampling Conference SWPSG Conference Sampling Conference SWPSG Conference Sampling Conference SWPSG Conference Maslij, Hnatyk Salamaga Szymkowiak Majewska Kowalczyk, Tomczyk Dehnel Kubacki, Grancow, Jędrzejczak Burkiewicz Wagner, Mantaj Gołata Wagner Klimanek Coffee break Coffee break Invited lecture: Tille Invited lecture: Longford Coffee break Coffee break Plikusas Szwarc Jakóbik, Ruta Trzpiot, Jeziorski Registration Krapavickaite Frodyma Zięba Sompolska-Rzechuła Kowalski Bąk, Wawrzyniak Ganczarek Lunch break Lunch break Lunch break Opening ceremony: Wywiał, Domański, Lysa Maslij Invited lecture: Ghosh Merad Orwat Gamrot Szczyt Coffee break Wywiał Paradysz Salvatore Szmuksta-Zawadzka, Zawadzki, Żądło Wolny, Szromek Kordos Jaguś Conference dinner Amicus club

5 Malay Ghosh University of Florida, BAYES AND EMPIRICAL BAYES BENCHMARKING WITH APPLICATIONS TO SMALL AREA ESTIMATION It is well-known that small area estimation needs explicit, or at least implicit use of models. These model-based estimates can differ widely from the direct estimates, especially for areas with very low sample sizes. One potential drawback of the model-based estimates is that when aggregated, the overall estimate for a larger geographical area may be quite different from the corresponding direct estimate, the latter being usually believed to be quite reliable. This is because the original survey was designed to achieve specified inferential accuracy at this higher level of aggregation. The problem can be more severe in the event of model failure as often there is no real check for validity of the assumed model. Moreover, an overall agreement with the direct estimates may sometimes be politically necessary to convince the legislators of the utility of small area estimates. One way to avoid this problem is the so-called benchmarking approach which amounts to modifying these model-based estimates so that one gets the same aggregate estimate for the larger geographical area. Currently the most popular approach is the so-called raking or ratio adjustment method which involves multiplying all the small area estimates by a constant factor so that the weighted total agrees with the direct estimate. It is not clear whether this method as such is guided by some firm statistical principle. We propose instead a constrained Bayesian approach to achieve the necessary benchmarking. The results are developed for area level models. Explicit Bayesian and empirical Bayes estimators are derived with benchmarking the weighted mean or benchmarking both the weighted mean and variability. The results are provided under a general decision-theoretic formulation. Keywords: Area-level, empirical Bayes, penalty parameter, weighted mean, weighted variability.

6 Yves Tillé University of Neuchâtel, BALANCED SAMPLING, PRINCIPLES, ALGORITHMS AND APPLICATIONS We present a review and assessment of the use of balanced sampling by means of the cube method. After defining the notion of balanced sample and balanced sampling, a short history of the concept of balancing is presented. The theory of the cube method is briefly presented. Emphasis is placed on the latest developments and applications of this algorithm. A list of applications is provided and is followed by a discussion of the interest of balanced sampling.

7 Nicholas T. Longford SNTL, Reading, England, and UPF, Barcelona, Spain, SMALL-AREA ESTIMATION WITH SPATIAL SIMILARITY We derive a class of composite estimators of small-area quantities that exploit spatial (distance-related) similarity. They are based on a distribution-free model for the districts,but the estimators are aimed to have optimal design-based properties. Composition is applied also to estimating some of the global parameters on which the small-area estimators depend. We show that the commonly adopted assumption of random effects is not necessary for exploiting the similarity of the districts (borrowing strength across the districts). The methods are applied to estimation of the mean household sizes in the counties (comarcas) of Catalonia. Key phrases: Composite estimation, design-based estimator, exploiting similarity, modelbased estimator, multivariate shrinkage, small-area estimation, spatial similarity.

8 Wojciech Gamrot Department of Statistics, University of Economics in Katowice, ON SAMPLING FROM OVERLAPPING STRATA WITH PRE-DETERMINED MINIMAL SAMPLING FRACTIONS In some surveys the population subsets of interest (strata) are overlapping. The survey of passenger loads carried out to study characteristics of communication lines operated by Municipal Transport Union of the Upper-Silesian Industrial District is a vivid example of such situation. This survey is also characterized by multiple objectives and specific requirements concerning sample representativeness, taking shape of minimum stratum sampling fractions. In this paper an approach to sample selection satisfying these requirements by using a genetic algorithm is presented.

9 Krzysztof Jakóbik, Grzegorz Ruta Statistical Office In Kraków, THE EFFECTIVENESS OF CATI METHOD IN THE SURVEY STRUCTURE OF AGRICULTURAL HOLDINGS The subject of the lecture is the survey Structure of agricultural holdings, which was carried out with the use of the following methods: computer assisted telephone interviewing (CATI), face-to-face interviewing, the Internet self-interviewing and the postal interviewing. Data were collected on the report/ questionnaire R-SGR The structure of agricultural holdings survey in June The scope of the survey included agricultural holdings used by natural persons and by legal persons. The paper presents basic rules, definitions and terms used in the survey, the sampling scheme and organization of the survey. The main part of the lecture brings up the comparison of applied methods of data collecting, evaluation of their effectiveness and completeness of the gained results. EFEKTYWNOŚĆ METODY CATI W BADANIU STRUKTURY GOSPODARSTW ROLNYCH Tematem referatu jest badanie struktury gospodarstw rolnych, które zostało przeprowadzone metodami wywiadu teleankieterskiego (CATI), bezpośredniego wywiadu ankieterskiego, samopisu internetowego oraz wywiadu pocztowego. Informacje zbierane były na sprawozdaniu/kwestionariuszu R-SGR Badanie struktury gospodarstw rolnych w czerwcu Omawiane badanie obejmowało gospodarstwa rolne osób fizycznych oraz gospodarstwa rolne osób prawnych i jednostek organizacyjnych niemających osobowości prawnej. W wystąpieniu omówione będą podstawowe zasady, definicje i pojęcia obowiązujące w badaniu, schemat losowania próby oraz organizacja badania. Zasadnicza część referatu poświęcona będzie porównaniu zastosowanych metod zbierania danych, ocenie ich skuteczności oraz kompletności uzyskanych wyników.

10 Jan Kordos Formerly Warsaw School of Economics, NEGLECTED FIELDS OF SAMPLE SURVEY DESIGN AND IMPLEMENTATION The author begins with the Deming s (1950) approach to survey design, and discusses different steps of survey design and implementation. He considers planning and preparatory work of survey design: defining major objectives, preparing first operation plans, method of data collection (questionnaire design), preliminary tabulation and analysis plans, frames and sample design, pre-test and pilot studies, preparing final survey documents; survey implementation (field work), data processing; analysis of survey data, publication and results dissemination. The author tries to prove the following fields are neglected: first steps of sample design (Kish, 1995, 1987); cooperation between different experts involved in sample design and implementation (Kish, 1989), analysis of survey data, data quality assessments (Brackstone, 1999; Linacre and Trewin, 1987). He presents some examples from his practice (Kordos, 2001). At the end some conclusions are given. References BRACKSTONE, G. (1999). Managing Data Quality in a Statistical Agency. Survey Methodology, Vol. 25, No. 2, DEMING, W.E. (1950), Some Theory of Sampling, New York: Wiley. EUROSTAT (2003), Definition of Quality in Statistics. Eurostat Working Group on Assessment of Quality in Statistics, Luxembourg, 2-3 October KISH, L. (1965), Survey Sampling, New York KISH, L. (1995), The Hundred Years Wars of Survey Sampling, Statistics in Transition, vol. 2, Number 5, pp KISH, L. (1987), Statistical Design for Research, New York: John Wiley and Sons. KISH, L. (1989), Sampling Methods for Agricultural Surveys, Rome: FAO. KORDOS, J. (2001). Some Data Quality Issues in Statistical Publications in Poland. Statistics in Transition, vol. 5, No. 3, pp LINACRE,S.J., TREWIN, D.J. (1989). Evaluation of errors and appropriate resource allocation in economic collection. Australian Bureau of Statistics, Statistical Services Papers, vol. 7, 1, s SäRNDAL, C-E., SWENSSON, B. WRETMAN, J. (1992). Model Assisted Survey Sampling. New York: Springer-Varlag. United Nations (1964). Recommendations for the Preparation of Sample Survey Reports (Provisional Issue). Statistical Papers, Series C, No. 1, Rev. 2. ST/STAT/SER.C/1/Rev.2. New York.

11 Barbara Kowalczyk, Emilia Tomczyk Warsaw School of Economics, SURVEY NON-RESPONSE AND PROPERTIES OF EXPECTATIONS OF INDUSTRIAL ENTERPRISES ANALYSIS BASED ON BUSINESS TENDENCY SURVEYS Expectations of economic agents exert unquestionable influence on their investment, employment, and production decisions. To analyse properties of expectations formation processes, direct data on expectations is needed. However, the main source of direct data on expectations business tendency surveys is plagued by non-response. Moreover, the non-response rates are much higher for questions about expectations than analogous ones about realizations. The missing-data mechanism is suspected to be not missing at random. So the problem of drawing conclusions about properties of expectations formation processes becomes particularly challenging. Our empirical analysis is based on business tendency surveys conducted by the Research Institute for Economic Development RIED of the Warsaw School of Economics. We propose to verify the hypothesis that expectations of Polish industrial enterprises are formed rationally. To this effect, we employ the Gourieroux Pradel (1986)1 test of rationality of expectations, based on contingency tables summarizing firm-level data collected by the RIED. Item non-response will be taken into account in the analysis, which can be considered a step towards obtaining broader and consistently more reliable conclusions in the field of examination of properties of expectations. 1 Gourieroux C., Pradel J. [1986] Direct test of the rational expectations hypothesis, European Economic Review 30:

12 Jan Kowalski Warsaw University of Technology, STATIONARY MODEL IN ROTATION SCHEMES We consider a sequence of surveys involving rotation of elements in the sample. For each occasion an optimal linear unbiased estimator (BLUE) of the current population mean, based on all available responses, may be found. Our object of interest are linear recurrence relations between the BLUE estimators obtained on successive occasions. Then each estimator may be computed recursively and at a reduced cost. We aim at finding explicit formulas for the solution. In its original version (see Patterson (1950)) the problem is formulated in a fairly general manner. However, an efficient method to obtain the solution is hard to find. We introduce a class of cascade patterns, meaning that the rotation scheme should have a sufficiently regular structure. Such a class contains in particular the Current Population Survey (CPS) and the Polish Labour Force Survey (BAEL). Moreover, we consider the stationary form of the recurrence. This in turn may be identified with passing to the limit with occasion number in the solution to the classical version. Our gain is the ability to apply a more convenient, algebraic approach to the optimization problem. The problem itself may then be reduced to selecting a certain subset of the set of all the roots of a polynomial with real coefficients. The results were obtained together with Jacek Wesołowski from the Central Statistical Office of Poland. Keywords: repeated surveys, rotation scheme, BLUE, linear recurrence, restricted least squares, linear equations References Binder, D.A., Hidiroglou M.A. (1988) Sampling in Time, Handbook of Statistics, 6, Kowalski, J. (2006) Rotation in sampling patterns, accepted for Journal of Statistical Planning and Inference Patterson, H. (1950) Sampling on successive occasions, Journal of the Royal Statistical Society B, 12, Rao, J., Graham, J. (1964) Rotation Designs for Sampling on Repeated Occasions, Journal of the American Statistical Association, 50,

13 Danutė Krapavickaitė Institute of Mathematics and Informatics, Vilnius, Lithuania, ESTIMATION OF SOME PROPORTION A proportion estimation problem for some two-stage sampling design is investigated. The situation is encountered in the Adult Education Survey (AES) when estimating the share of individuals in non-formal education involved in job-related learning activities. 1 Population and parameter. Let us denote by U { u, 1 = 1 u2,..., u N } the population of the units, to each of which a cluster of subunits of size M i, i=1,2,,n, is associated. Thus, the population of all subunits U 2 consists of M = M M N elements. Suppose some of the subunits have an attribute of interest, and some of them do not have it. Let us introduce a study variable z in population U1 with value z i = 1, if there is at least one subunit with the attribute among M subunits associated with the unit u, and z = 0 otherwise, i=1,2,,n. i Then the share (proportion) of the units in attribute is equal to the mean of variable z: N μ = t / N = z N. z z i = 1 i U 1 i i having associated at least one subunit with the 2 Sample and estimator. Let the sample design of subunits constituting population U 2 is described by a 2-stage sampling design with some probabilistic sample of units in U at the first stage and a simple random sample of mi, associated with unit u i at the second stage: s = s. U i s I IIi U 2 s IIi i i s I 1 m M, subunits in the cluster The design-based estimator used often for the share of units having associated at least one subunit with the attribute, is ˆ μ z = tˆ z / N, tˆ z = di zˆ i. i: i s I Here di is a 1st stage sampling design weight, ẑi is the design-based estimator of zi : z ˆ i = 1 if at least one subunit with the attribute belongs to s IIi, and z ˆ i = 0 otherwise. This estimator is biased. The new estimator will be suggested.

14 Jan Kubacki 2, Bartosz Grancow 1, Alina Jędrzejczak 3 AN EXAMPLE OF EMPIRICAL BEST LINEAR UNBIASED PREDICTOR (EBLUP) APPLICATION FOR SMALL AREA ESTIMATION IN POLISH HOUSEHOLD BUDGET SURVEY In article results for small area estimation using empirical best linear unbiased predictor (EBLUP) for data from Polish Household Budget Survey is presented. These results is related to several variables describing household income obtained for regions using small area models. Estimation of sample errors was conducted by balanced repeated replication technique. EBLUP estimates and MSE estimates was carried out using variance components techniques. Two methods of MSE estimation was used maximum likelihood (ML) and restricted maximum likelihood (REML) algorithms. The computation was made using SAE package designed for R-project environment. PRZYKŁAD ZASTOSOWANIA EMPIRYCZNYCH NAJLEPSZYCH NIEOBCIĄŻONYCH PREDYKTORÓW LINIOWYCH (EBLUP) W SZACUNKACH DLA MAŁYCH OBSZARÓW DLA BADANIA BUDŻETÓW GOSPODARSTW DOMOWYCH W pracy przedstawiono wyniki estymacji dla małych obszarów wykonane techniką empirycznych najlepszych nieobciążonych predyktorów liniowych (EBLUP) dla danych z Badania Budżetów Gospodarstw Domowych. Przedstawione rezultaty dotyczą kilku zmiennych opisujących dochód gospodarstwa domowego oszacowanych dla województw z użyciem modeli dla małych obszarów. Szacunki wariancji dla estymatorów bezpośrednich wykonano przy użyciu techniki zrównoważonych powtarzalnych replikacji (BRR) zaś szacunki wartości dla estymatora EBLUP oraz jego wariancji wykonano stosując metodę komponentów wariancyjnych, przy czym zastosowano dwa warianty metod estymacji z użyciem metody największej wiarygodności (ML) oraz metody największej wiarygodności z ograniczeniami (REML). W obliczeniach wykorzystano pakiet SAE będący częścią środowiska R-project. 2 Urząd Statystyczny w Łodzi, Ośrodek Realizacji Badań, ul. Suwalska 29, Łódź, Poland, j.kubacki@stat.gov.pl 3 Uniwersytet Łódzki, Wydział Ekonomiczno-Socjologiczny, Katedra Metod Statystycznych, ul. Rewolucji 1905 r. 41, Łódź, Poland, jedrzej@uni.lodz.pl

15 Olha Lysa Department of Social and Demographic Statistics, Institute for Demography and Social Research, National Academy of Sciences of Ukraine, APPROACHES TO IMPROVING OF MONTHLY LFS ESTIMATES RELIABILITY The paper presents main results of investigations on problem of reliable estimation of monthly labour force indicators for regional and local level by the Ukrainian LFS data. The approach to estimator construction based on the monthly composite estimation method is considered. The results of LFS in Ukraine are used as information base for economical situation analyzing, social-economical processes modeling, and administrative decisions acceptance. Thus information necessity exists both on international, and at the state, regional and local levels. According to modern international standards of statistical information quality, one should be characterized by the maximal completeness and timeliness, be relevant to users needs, reliable, accessible, and clear, comparable, coordinated with available data from other sources. Main characteristics of the LFS in Ukraine are: stratified, multistage, random sample; representation of all regions, proportionally to number of population; monthly frequency of surveys from 2004; monthly sample size is 11.1 thousand households; persons year old are interviewed about their economical activity during the previous week; used rotation scheme there are 6 rotational groups, every month two of them are replaced by one new group and one that has been surveyed in corresponding month of the last year; estimates are calculated for population, the statistical weights system takes into account the sample design, refusal rates, external data sex-age structure of population by demographic statistics. The LFS, by results of which in-labour force, employment and unemployment indicators are measured, mainly provide an opportunity of their reliable estimation on the nation-wide level. The estimates received for lower levels in many cases are insufficiently reliable and demand using of special approaches for more precise estimation. As one of way to solving this problem in Ukrainian official labour force statistics is used the method of monthly composite estimation which takes into account the rotation scheme. The composite estimator is based on the direct estimator for current month, the composite estimator for previous month, and the estimator of indicators changing between consecutive months that are received on the basis of 4 rotation groups LFS data, which are common for current and previous months. For every domain are calculated the employment, unemployment levels by composite model and the non-in-labour force level as difference between population number and sum of estimated employment and unemployment levels. Results of application of the method of monthly composite estimation show the effectiveness of using of this approach for reliability improvement of LFS estimates. The last application of this method for LFS data 2007 increase the accuracy of employment and unemployment levels estimation in average on the 19,6 % and 33,3 % accordingly for all domains. The research in direction of reliability improving of labour force estimates for the regional and local levels in Ukraine are on the whole on the initial stage. Although application of

16 composite estimation methods allows to attain positive results, but for more complete decision of problem of reliability the necessary use of additional information and more effective models. More powerful approaches which will be developed in Ukraine are built on time series and cross-sectional models. REFERENCES 1. Ghosh M., Rao J. N. K. Small Area Estimation // An Appraisal, Statistical Science Vol. 9, 1. P Design and Methodology. Current Population Survey: Technical Paper. Washington: U.S. Department of Labor, BLS, p. 3. Rao J.N.K. Small Area Estimation. New York: Wiley, p.

17 Masliy Vadym Volodymyrovych, Hnatyk Yaroslav Bohdanovych Ternopil National Economic University, THE THEORETICAL AND METHODOLOGICAL BASIS OF CONDUCTING THE SELECTIVE REVIEWS OF MOTOR TRANSPORT CONVEYANCES AND THE ANALYSIS OF INCOMPLETE DATA The market of motor transport services is a specific indicator of the national economy status in general. The services offer level in this sphere characterizes the development of the whole economy infrastructure and the demand for cargo and passenger motor transport services informs about the prosperity and the level of mobility of the nation. The transition to the new phase of the stable social economic development in Ukraine and the course to the European integration require the outstripping development of the whole transport system of the country. Under the conditions of intensive increase of the number of economic subjects of various ownership forms in the sphere of motor transport conveyances rises the need in efficient, entire and qualitative information about the number of both cargo and transport conveyances. Owing to this fact, there is the necessity of conducting analysis of incomplete data. The selective reviews in the sphere of motor transport services are carried out in a form of anonymous questionnaires. The day before surveys the officials of the national statistics agencies together with the transport department of local administration give general instructions to all the entrepreneurs dealing with the commercial cargo transport conveyances who will be submitted to surveys, concerning its aim and the procedure of filling out the questionnaires. Some difficulties could be encountered in survey by questionnaires while compiling the information, defining the reviews scale and forming the informational databases (the statistical agencies, tax administration, transport department and state patrol duty service databases can differ). The main problem, which is not recognized by the statistical administration, is the processing of the questionnaire with incomplete information. Main types of mistakes made while carrying out the surveys are highlighted and classified in the article. The main existing approaches to the analysis of incomplete data are explored.

18 Salah Merad Office for National Statistics, UK, EVALUATING METHODOLOGICAL CHANGES IN THE ONS BUSINESS REGISTER AND EMPLOYMENT SURVEY USING A PILOT SURVEY The Business Register and Employment Survey (BRES) will replace two surveys: the annual employment survey, called ABI/1, and the Business Register Survey (BRS). Even though the sampled units in BRES are enterprises, BRES will collect data at local unit level, which should improve the quality of regional estimates. The current employment survey collects data at enterprise level, and in order to obtain regional estimates the returns are apportioned between local units using prediction rules based on a model. In the new integrated survey we have made several changes, both to the questionnaire and to the sampling and estimation methodology. The questionnaire changes include: rewording of questions, introduction of routing questions, dropping of gender employee count, and the addition of a monthly turnover question). Compared with the current annual employment survey, the changes to the sample design include the use of Full Time Equivalent employment as a stratifier, instead of total employment, and the complete enumeration of complex businesses (those active in different industries or regions). The estimation methodology for all the variables, with the exception of gender employment splits, is based on calibration to the main industry groups and regions. For the gender splits statistics we have developed a methodology that uses data from an external data source, the Annual Survey of Hours and Earnings. In 2008 we will send both BRS and BRES questionnaires to the BRS sampled businesses, each sampled enterprise receiving either one or the other. Data from the split sample will be used to assess the quality of the data from BRES, to evaluate the impact of each of the changes on employment estimates, when BRES replaces ABI/1 in 2009, and to estimate the discontinuity in the employment estimates. In this paper we outline the methodological changes, describe the sample design of the 2008 split BRS/BRES pilot, and present the evaluation plan we have developed to assess each of the changes. The current employment survey and BRES have different designs; we will discuss the issues that this raises when assessing the impact of the changes using statistical tests.

19 Aleksandras Plikusas Institute of Mathematics and Informatics, Vilnius, Lithuania, ON SOME RATIO TYPE ESTIMATORS OF THE FINITE POPULATION TOTAL Many estimators of the finite population parameters are constructed using known auxiliary variables. The classical well-known ratio estimator is one of them. Various improvements of this ratio estimator are considered by many authors. Some estimators use two auxiliary variables. The other group of estimators is composite estimators. Composite estimators are constructed by taking a weighted sum of Horvitz-Thompson estimator and some ratio type estimator. The sum of corresponding weights need not equal to one. The product estimator is effective in case negatively correlated auxiliary variable is available. This estimator behaves similarly as simple ratio estimator. In case one positively and one negatively correlated auxiliary are known, ratio-cum-product estimator (Singh (1969)), and dual to ratio-cum-product estimator (Singh et al (2005)) can be considered. The dual variables and dual estimators in the papers mentioned above were defined for simple random sampling without replacement. It was also shown that dual estimator in general is more effective compare to the ratio-cum-product estimator. In this paper the dual variables for the construction of dual to ratio-cum-product estimator, are defined for the case of stratified simple random sample and arbitrary sample design. In the case of simple random sampling, the dual variable has a nice property. If the correlation coefficient ρ(y,x) between study variable y and auxiliary variable x is equal to a, then the correlation coefficient ρ(y, x ) between variable y and variable x, dual to the variable x, is equal to a. Unfortunately this property of dual variable is not valid for more complicated sampling designs. In spite of this fact, the dual variables can be used to define dual to ratiocum-product estimator for the unequal probability sampling designs. In the case of stratified simple random sampling, separate dual to ratio-cum-product estimator may be also considered. References Bandyopadhyay, S. (1980) Improved ratio and product estimators. Sankhyā Series C, 42(2), Singh, M. P., (1969) Comparison of some ratio-cum-product estimators, Sankhyā Series B, 31, Singh, H.~P., Singh, R., Espejo, M.~R., Pineda, M.~D., Nadarajan, S. (2005) On the efficiency of the dual to ratio-cum-product estimator, Mathematical Proceedings of the Royal Irish Academy, 105A(2), Srivenkataramana, T. (1980) A dual to ratio estimator in sample surveys. Biometrika, 67,

20 Renato Salvatore University of Cassino, Italy, SELECTION OF COVARIATES IN SMALL AREA ESTIMATION WITH MULTILEVEL MODELS Mixed models can easily accommodate statistical relations between survey parameters and small-area predictors, in order to provide indirect estimation of small domain-level statistics. Moura and Holt (1999) introduced two-level models, that integrates the use of regressionsynthetic estimators and area level covariates into a single model. A more complex feature of such a model (respect to the basic small area models) is that a two-level mixed model allows for differences between slopes as well as the intercepts across small areas, and, in general, multilevel model (ML) involves the potential of the use of auxiliary information at both the unit and small area level. One of the advantages in using ML models over regression models is to recognize that small areas share common features. The small areas are not completely independent as could be assumed by using a separate linear regression model for each small area. With random coefficients we can model intercept and slope parameters in terms of area level covariates. There is a significant reduction of all the components of variance estimates after introducing explanatory area covariates Z, but in practice area-level covariates are more difficult to find that unit-level covariates (Rao, 2003). In the situation of no good area level explanatory variables, ML respect to standard unit level models can only avail of major flexibility in modelling, due to the presence of random slopes. If W is the complete set of variables in the available data, we currently partition W in the subset U, the unit level regression covariates, and A, the subset of remaining variables. In the situation in which there are no right area-level predictors, we discuss on replacing the original candidate area covariates in A with some of their linear transformations, in order to reduce variance components in the model, and in consequence the mean squared error of the model-based empirical estimator (Salvatore and Russo, 2008). We further analyze the reduction of components in the estimated mean squared error of the empirical predictor, related with the variations in model covariance parameters of random-area effects and residual, based on these linear transformations. The simulation study consists on analyzing the mean squared error and the absolute relative error of the mean estimates by selecting samples of farms from the population of the Italian Agricultural Census, where the estimation problem is related to find estimates of the average working days at municipality level. We compare efficiency of several small area models, like traditional unit-level and ML with and without covariates, and ML with explanatory arealevel covariates such as original and their transformed values. ML models variance components estimates are obtained by restricted maximum likelihood (REML) estimation method. Keywords: small area estimation, multilevel mixed models, restricted maximum likelihood estimation. References Moura, F.A.S., Holt D. (1999), Small Area Estimation Using Multilevel Models, Survey Methodology, 25, 1, Rao J.N.K. (2003), Small Area Estimation, Wiley, New York. Salvatore R., Russo C. (2008), Data Reduction in Small Area Estimation, Proceedings of the XLIV Meeting of the Italian Statistics Society.

21 Marcin Szymkowiak University of Economics in Poznań, CALIBRATION ESTIMATORS IN SURVEYS WITH NONRESPONSE Small Area Estimation (SAE) involves methods of estimation using all possible sources of information (registers, censuses) in a case where sample size is too small to obtain reliable results. In recent years a lot of attention in SAE has been paid to estimation with nonresponse. One of the method which became very important in surveys with nonresponse is calibration which was first introduced by Deville and Särndal (1992). Calibration as a method of treatment nonresponse rely on finding calibrated weights by using auxiliary information and minimizing a distance measure between the sampling weights and the new weights so that to satisfy certain calibration constraints. The main goal of this article is to present some aspects of calibration for quantilies according to models introduced by T. Harms and P. Duchesne (2006) using the calibration paradigm in connection with surveys with nonresponse. Deville J-C., Särndal C-E. (1992), Calibration estimators in Survey Sampling, Journal of the American Statistical Association, Vol. 87, Harms T., Duchesne P. (2006), On Calibration Estimation for Quantiles, Survey Methodology, Vol. 32, June Särndal C-E., Lundström S. (2005), Estimation in Surveys with Nonresponse, John Wiley & Sons, Ltd. ESTYMATORY KALIBRACYJNE W BADANIACH STATYSTYCZNYCH Z BRAKAMI ODPOWIEDZI Statystyka małych obszarów (SMO) obejmuje metody estymacji z wykorzystaniem wszelkich istniejących zasobów informacji (różnego rodzaju rejestrów administracyjnych, spisów, wykazów itd.) w przypadku, gdy liczebność próby jest niewystarczająca dla uzyskania wiarygodnych ocen szacowanych parametrów. W ostatnim czasie, dużo uwagi w SMO, przywiązuje się estymacji parametrów w populacji generalnej w przypadku gdy w badaniu występują braki odpowiedzi. Szczególne znaczenie odgrywa tutaj kalibracja, która jest nowoczesną metodą szacowania parametrów, w badaniach reprezentacyjnych z brakami odpowiedzi. Jej idea polega na skorygowaniu (odpowiedniej kalibracji) wyjściowych wag wynikających ze schematu losowania jednostek do próby, w taki sposób, aby skompensować utratę informacji związaną z brakiem danych. Korekty wag dokonuje się z uwzględnieniem zmiennych pomocniczych, które mogą pochodzić z tej samej próby co zmienna szacowana, bądź z różnych innych źródeł. Celem artykułu jest omówienie wybranych aspektów kalibracji dla kwantyli zgodnie z modelami przedstawionymi przez T. Harmsa i P. Duchesne (2006) w odniesieniu do badań statystycznych z brakami odpowiedzi. Deville J-C., Särndal C-E. (1992), Calibration estimators in Survey Sampling, Journal of the American Statistical Association, Vol. 87, Harms T., Duchesne P. (2006), On Calibration Estimation for Quantiles, Survey Methodology, Vol. 32, June Särndal C-E., Lundström S. (2005), Estimation in Surveys with Nonresponse, John Wiley & Sons, Ltd.

22 Wiesław Wagner University of Information Technology and Management in Rzeszów, THE REPRESENTATIVE METHOD In RESEARCH OF THE DOMESTIC TOURISM ACCORDING TO UN WTO The proper selection of statistical units from the general population to the attempt is one of prior assignments to become clear of statistical regularities appearing in mass-occurrences occurrent among other things in the tourism. Business entity working in different lines in the tourism, the recreation and the physical education, the public administration and territorial and trade organizations helping the tourist activity are interested in performance of such research. The set of potential units of the research determines the general population. They refer to real or hypothetical communities, favoured under certain conditions spatial-temporary. Units determine the immediate object and the subject of the statistical research, and to their description it use the arrangement of statistical features about the character qualitative or quantitative. On the job it introduced considerations concerning receivings of the representative sample from the general population in the light of research making in the domestic tourism. The World Organization of the Tourism (UN WTO - Union National World Tourism Organization) was presented suitable guidelines of such conduct. For this purpose it gave several general comments about the domestic tourism and investigated units, and then it exchanged manners of the qualification of the size of the attempt and her equations, and also it exchanged different indicators consequential from the enlargement of findings with the method representative in the domestic tourism. In some cases it enclosed illustrative examples. METODA REPREZENTACYJNA W BADANIACH TURYSTYKI KRAJOWEJ WEDŁUG UN WTO Właściwy dobór jednostek statystycznych z populacji generalnej do próby jest jednym z ważniejszych zadań przy wyjaśnianiu prawidłowości statystycznych przejawiających się w zjawiskach masowych występujących m. in. w turystyce. Wynikami takich badań zainteresowane są podmioty gospodarcze działające w różnych branżach w turystyce, rekreacji i kulturze fizycznej, jak również władze administracji publicznej i terytorialnej oraz organizacje branżowe wspomagające działalność turystyczną. Zbiór potencjalnych jednostek badania stanowi populację generalną. Odnoszą się one do rzeczywistych lub hipotetycznych zbiorowości, wyróżnionych w określonych warunkach przestrzenno-czasowych. Jednostki stanowią bezpośredni przedmiot i podmiot badania statystycznego, a do ich opisu wyróżnia się układ cech statystycznych o charakterze jakościowym lub ilościowym. W pracy przedstawiono rozważania dotyczące pobierania próby reprezentacyjnej z populacji generalnej w świetle badań prowadzonych w turystyce krajowej. Odpowiednie wytyczne takiego postępowania zostały podane przez Światową Organizację Turystyki (UN WTO Union National World Tourism Organization). W tym celu podano kilka ogólnych uwag o turystyce krajowej i badanych jednostkach, a następnie wymieniono sposoby określenia wielkości próby i jej wyrównywania, a także wymieniono różne wskaźniki wynikające z rozszerzenia wyników badań metodą reprezentacyjna w turystyce krajowej. W niektórych przypadkach zostały dołączone przykłady ilustrujące.

23 Andrzej Mantaj, Wiesław Wagner University of Information Technology and Management in Rzeszów, COMMENTS ABOUT THE FORMULA BELONGINGS OF UNITS THE SECOND ROW IN THE SCHEMA OF THE DRAW SIMPLE WITH RETURNING On the job it make general mathematical model the schema of the draw with returning. For this models it introduced on the number of attempts expressed by the number of the variation with repetitions, the probability of drawing by lot of attempts with given element and one gave formulas on probabilities belongings I- and II-the kind for which one made suitable removals. The formula on the membership II-the kind was shown two manners. Mentioned examples were illustrated with formulas. UWAGI O WZORZE PRZYNALEŻNOŚCI JEDNOSTEK RZĘDU DRUGIEGO W SCHEMACIE LOSOWNIA PROSTEGO ZE ZWRACANIEM W pracy podano ogólny model matematyczny schematu losowania ze zwracaniem. Przedstawiono dla niego wzory na liczbę prób wyrażoną przez liczbę wariacji z powtórzeniami, prawdopodobieństwo wylosowania prób z zadanym elementem oraz podano wzory na prawdopodobieństwa przynależności I- i II-rodzaju, dla których dokonano odpowiednie wyprowadzenia. Wzór na przynależność II-rodzaju został wykazany dwoma sposobami. Wymienione wzory zilustrowano przykładami.

24 Janusz L. Wywiał Department of Statistics, University of Economics in Katowice, ASSESSING TOTAL IN SMALL AREA SAMPLING BY MEANS OF TEST- PREDICTOR Our purpose is prediction a total in a population. In order to do it we can use the following two predictors. The first one is a sample mean (drawn from the population) multiplied by the size of the domain. The second one is a subsample (from the domain) mean multiplied by the size of the domain. It is well known that the both predictors are unbiased if the expected values of variables in the domain and in the population are the same but the mean square error of the first predictor (based on the sample mean) is not larger than the mean square error of the second predictor (based on the subsample mean). Hence, we should use the first predictor provide the expected value of the population mean is equal to the expected value of the domain mean. So, the hypothesis that these both expected values are the same can be formulated. If the hypothesis is true we use the first predictor otherwise we use the second one. In the paper the mean square error of the defined predictor is evaluated.

25 Agnieszka Zięba Warsaw School of Economics, POVERTY INDICATORS ESTIMATION AT NUTS 4 LEVEL The most significant obstacles to achieving real integration, which is an object of special concern and support of the European Union cohesion policies, are counteracting problems of poverty. To take effective preventive actions, it is essential to carry out both national and regional level an analysis based on measurable and clearly interpreted indicators. It would be desirable that a system of appropriate indicators was applicable also on higher levels of spatial disaggregation. For Poland this means the level of district (powiat) corresponding to NUTS4 areas in Eurostat nomenclature. It is, however, impossible to achieve reliable values of poverty indicators in a classical way due to the fact that they can only be calculated on the basis of available data from surveys carried out by the Central Statistical Office. In these surveys the numbers of individuals and households at the district level are negligible or even nil which results in these indicators being useless in evaluation of poverty phenomena. The purpose of this paper is to propose a solution of this problem with respect to some Laeken indicators by using Small Area Estimation (SAE) techniques. The SAE techniques depend on borrowing strength from external datasets, such as administrative databases or other surveys. The proposed methodology is based on area level random effect models that are used when auxiliary information is available only at area level. The paper will in detail present not only the Empirical Best Linear Unbiased Predictor (EBLUP), but also the problems that have to be solved before the EBLUP can be used for estimation with use of data taken from EU SILC researches. To produce small area estimates using an EBLUP procedure, calculating direct estimator for every district is necessary. The lack of researched units for some districts and appropriate method of imputation will be also discussed. ESTYMACJA WSKAŹNIKÓW UBÓSTWA NA POZIOMIE POWIATÓW Jedną z podstawowych barier w osiąganiu integracji, która stanowi cel strategiczny Unii Europejskiej jest problem ubóstwa. Wobec potrzeby przeciwdziałania jego przejawom niezbędne jest posługiwanie się mierzalnymi i jednoznacznie interpretowalnymi wskaźnikami, które umożliwiają porównywanie krajów i regionów. Istotne jest również wychwycenie lokalnego wymiaru badanych zjawisk w przypadku Polski wymiar ten stanowią powiaty. Dla tak wysokiego szczebla dezagregacji przestrzennej uzyskiwanie odpowiednich wskaźników okazuje się niemożliwe przy zastosowaniu podejścia klasycznego. Wskaźniki ubóstwa bowiem w dużej części konstruowane są na podstawie badań ankietowych, w których liczebność próby na stopniu lokalnym jest zbyt niska. Uzyskiwane dla powiatów estymatory cechuje duży błąd szacunku, który uniemożliwia wnioskowanie na ich poziomie. Referat przedstawia propozycję rozwiązania powyższego problemu w przypadku wybranych wskaźników lejkenowskich przy zastosowaniu metod statystyki małych obszarów, które umożliwiają zapożyczanie mocy z danych dodatkowych, pochodzących z dostępnych rejestrów lub z innych badań. Proponowana metodologia bazuje na modelu mieszanym z efektem losowym na poziomie obszaru. Przy zastosowaniu takiego modelu możliwa estymacja w przypadkach, gdy dodatkowe informacje dostępne są jedynie na poziomie rozpatrywanego obszaru.

26 W pracy omówiony zostanie szczegółowo Empiryczny Najlepszy Nieobciążony Predyktor Liniowy (EBLUP) oraz problemy, które należy rozwiązać jeśli chcemy go użyć do omawianych zagadnień przy wykorzystaniu danych z badania EU-SILC. Poruszony zostanie temat uzupełniania braków w przypadku estymatorów bezpośrednich, które są niezbędne do estymacji metodą EBLUP, a które dla niektórych powiatów są niemożliwe do wyznaczenia ze względu na brak jednostek badanych w tym obszarze.

27 Tomasz Żądło Department of Statistics, University of Economics in Katowice, ON PREDICTION OF DOMAIN TOTAL BASED ON UNBALANCED LONGITUDINAL DATA Although in sample surveys the problem of estimation of population characteristics is usually the key issue, clients may also be interested in subpopulations (domains) characteristics. In the model approach two types of models are considered: type A assumed for the direct domain estimates and type B assumed for random variables which realizations are values of the variable of interest. Best Linear Unbiased Predictor (BLUP) may depend on unknown model parameters which can be replaced by their estimates to obtain Empirical Best Linear Unbiased Predictor (EBLUP) which remains unbiased under some assumptions. Many surveys are repeated in time what gives a possibility to use information from past periods to increase accuracy of prediction for the current period. In small area estimation literature many papers on prediction of domain total based on type A models assumed for longitudinal data are available. Although there are many papers and monographs on type B models for longitudinal data, the problem of prediction of domain total under these models is not studied extensively. In the paper the problem of prediction of domain total assuming some model, which belongs to the class of type B General Mixed Linear Models for longitudinal unbalanced data, is studied. The formulae of EBLUP, its MSE and the MSE estimator are derived.

28 Dorota Bartosińska Warsaw School of Economics, Konrad Cuch Statistical Office in Warsaw, Czesław Domański Uniwersytet Łódzki Waldemar Dubla Statistical Office in Łódź, Wojciech Gamrot Department of Statistics, University of Economics in Katowice, Malay Ghosh University of Florida, Stanisław Heilpern University of Economics in Wrocław, Aurelia Hetmańska Statistical Office in Katowice, Krzysztof Jakóbik, Statistical Office in Kraków, Irena Kasprowicz-Ruka Warsaw School of Economic, Jan Kordos Formerly Warsaw School of Economics, Barbara Kowalczyk Warsaw School of Economics, Jan Kowalski Warsaw University of Technology, Danutė Krapavickaitė Institute of Mathematics and Informatics, Vilnius, Lithuania, Jan Kubacki Statistical Office In Łódż, Alina Jędrzejczak University of Łódź, Nicholas T. Longford SNTL, Reading, England, and UPF, Barcelona, Spain, Olha Lysa Department of Social and Demographic Statistics, Institute for Demography and Social Research, National Academy of Sciences of Ukraine, Vadym Volodymyrovych Masliy Ternopil National Economic University, Ukraine, Salah Merad Office for National Statistics, UK, Aleksandras Plikusas Institute of Mathematics and Informatics, Vilnius, Lithuania, Joanna Pieśniewska TNS OBOP, Paweł Predko TNS OBOP, Grzegorz Ruta Statistical Office In Kraków, Renato Salvatore University of Cassino, Italy, Marcin Szymkowiak University of Economics in Poznań, Yves Tillé University of Neuchâtel, Wiesław Wagner Rzeszów University of IT and Management