ŚLĄSKI PRZEGLĄD STATYSTYCZNY

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1 Polskie Towarzystwo Statystycze Oddział we Wrocławiu ŚLĄSKI Silesia Statistical Review Wydawictwo Uiwersytetu Ekoomiczego we Wrocławiu Wrocław 2o11

2 RADA NAUKOWA Walety Ostasiewicz Tadeusz Bedarski, Luisa Caal, Staislava Hroová, Katarzya Ostasiewicz, Agiola Pollastri, Emilia Zimkova KOMITET REDAKCYJNY Walety Ostasiewicz (redaktor aczely) Zofia Rusak (zastępca redaktora aczelego) Edyta Mazurek (sekretarz aukowy) Tadeusz Borys, Staisław Heilper, Jausz Wywiał ADRES REDAKCJI Katedra Statystyki Uiwersytetu Ekoomiczego we Wrocławiu ul. Komadorska 118/120, Wrocław tel. (71) , tel./fax (71) Publikacja jest dostępa a stroie Streszczeia opublikowaych artykułów są dostępe w międzyarodowej bazie daych The Cetral Europea Joural of Social Scieces ad Humaities oraz w The Cetral ad Easter Europea Olie Library Iformacje o aborze artykułów i zasadach recezowaia zajdują się a stroie iteretowej Wydawictwa

3 Spis treści Od redakcji 5 Wolfgag Glatzer, Gefühlte (U)Gerechtigkeit 7 Jacek Szołtysek, Grażya Trzpiot, Klasyfikacja oczekiwań i preferecji komuikacyjych studetów 21 Agieszka Tarowska, Regioale zróżicowaie kapitału ludzkiego w Polsce w latach Walety Ostasiewicz, Professor Zdzisław H. Hellwig. O the occasio of his 85 th birthday 57 Katarzya Ostasiewicz, Uikąć tragedii wspólego pastwiska ekoomiczy Nobel 2009 dla Elior Ostrom 69 Edyta Mazurek, Applicatios of Mathematics ad Statistics i Ecoomy. The 13 th Iteratioal Scietific Coferece Scietific Statistical Semiar Marburg-Wroclaw, Marburg, September 26 29, Exteded summaries of selected papers 83 Agata Girul, Ważiejsze dae o województwach 111 Summaries Wolfgag Glatzer, (Nie)sprawiedliwość odczuwaa 20 Jacek Szołtysek, Grażya Trzpiot, Classificatio of trasport service expectatios ad prefereces of studets 31 Agieszka Tarowska, Regioal diversificatio of the huma capital i Polad i the years

4 PROFESOR ZDZISŁAW H. HELLWIG. ON THE OCCASION OF HIS 85 TH BIRTHDAY ŚLĄSKI Walety Ostasiewicz Uiwersytet Ekoomiczy we Wrocławiu ISSN Brief biography Prof. Dr. hab. h.c.h.c. Z.H. Hellwig was bor o 26 May 1925 i a small tow Dokszyce ot for away from Wilo. Both of his parets were teachers. His father Hery Hellwig taught the Germa laguage, ad his mother taught the mathematics. Prof. Z. Hellwig was educated at Kig Zygmut August School i Wilo. The secodary school graduatio certificate (matura, i Polish) he obtaied however after the Secod World War i Wrocław i He obtaied his bachelor degree i Warsaw where he studied uder the well-kow Polish ecoomist Professor Oskar Lage. I 1952 he received his Master Degree (magister, i Polish) at SGPiS (The School of Plaig ad Statistics) i Warsaw. Beig the studet of the secod year i the Higher Commercial School (Wyższa Szkoła Hadlowa i Polish) he started to work at this School as a youger assistat. O the basis of the work Liear regressio ad its applicatios i ecoomics he got i 1958 his Ph.D. degree i ecoomic scieces. The followig year he came to Eglad at the ivitatio of Mr. Reddaway, Director of the Departmet of Applied Ecoomics, Uiversity of Cambridge ad studied mathematical ecoomics ad statistics i Lodo ad Cambridge. I 1967 he became the Professor i ecoomics, ad sice 1972 he is the Ordiary Professor i ecoomics. I 1962 Prof. Z. Hellwig was omiated the Head of Departmet of Statistics ad held this positio till 1995, this is to the year whe he retired. Besides beig the Head of Departmet, Professor Hellwig performed a umber of duties. For three times he served as the vice-

5 ŚLĄSKI 58 Walety Ostasiewicz Rector, he was also the Dea of the Faculty, editor-i-chief of the Research Papers of Wrocław School of Ecoomics. Professor Hellwig was the foudig editor of the prestigious Polish joural Operatios Research ad Decisios, ad is still active as a vice-chair of the Scietific Committee. Professor Hellwig holds a umber of awards, icludig Miistry awards, prestigious award by the Prime Miister of Polish Govermet, the Medal from Polish Statistical Society. Amog his may hoors, he received a hoorary doctorate from Cracow Uiversity of Ecoomics i 1985, ad from Prague Uiversity of Ecoomics i He was elected as the hoorary member of the Polish Academy of Sciece Committee for Statistics ad Ecoometrics. Professor Hellwig ejoys discussios, especially with his frieds ad youg people frieds. For hours log he is able to chat o ay subject, icludig politics, ecoomy, sex, mathematics, philosophy, ad history. He was, ad he still is, admired, respected ad loved. Professor Hellwig has authored or edited may books, ad roughly 250 papers. The works o the variable selectio ad o the measure of socio-ecoomic developmet are the most cited, ad most ifluetial papers i applied statistics. 2. Regressio aalysis The problem of regressio is probably the oly scietific problem which Professor Hellwig studied durig his whole scietific life. To this problem he devoted his doctoral thesis, it costituted the core of his habilitatio dissertatio, he published may papers o this subject. Professor Hellwig itroduced a ew defiitio of the regressio cocept. The ew defiitio is give as follows. Let a ad b be ay real umbers which satisfy the relatio: b a f x, y dx dy 1, where f(x, y) is a desity fuctio, ad α is ay small umber from the iterval [0, 1].

6 85 th birthday of Profesor Zdzisław H. Hellwig 59 ŚLĄSKI The regressio is defied as a set R k of fuctios ψ(x, α 1, α 2,, α k ), such that the followig relatio: P b Y x f xy x a, b x x dxdy 1 a is satisfied for some big umber Δ. Simplified versio of this relatio is the followig: P x a, b x Y x Hellwig s method of variable selectio I the paper o variable selectio (see [Hellwig 1968]) the measure for evaluatig the iformatioal capacity of exogeous variables i ecoometric model was itroduced. Let X () = {X 1, X 2,, X } be a set of potetially possible variables which ca be used for the predictio of aother variable by meas of liear predictor of the form: Y a a X... a X The problem is to determie the most iformative m-elemet subset X X, X,..., X } of the give set X (). ( m) { i1 i2 im k, 1 k2 The crucial subproblem is the defiitio of the appropriate measure of the iformatio coveyed by the chose variables. The iformatio measure coveyed by the m-elemet subsets { X X,..., X } of the potetial variables {X 1, X 2,, X } has bee defied by the followig formula: H ( m, k,) m m i1 j1 r 2 ki r kik j,. k m where: k = (k 1, k 2,, k m ), r the correlatio coefficiet betwee k i k j X ad X k, j k i

7 ŚLĄSKI 60 Walety Ostasiewicz r k i the correlatio coefficiet betwee Y ad X k i. This measure tured out to be extremely useful i practical applicatio. 4. Hellwig s measure of developmet Oe of the biggest achievemets of Prof. Hellwig is the famous, ow the so-called Hellwig s measure of developmet. This measure has bee defied for solvig the followig problem. Suppose there is give some fiite set of N etities, such that coutries or regios, which are characterized by variables X 1, X 2,, X. Let symbol x ij, i = 1, 2,, N, j = 1, 2,, deote the value of the j-th variable for the i-th etity, or object. The problem is to determie the level of the ecoomic developmet for each etity (object) uder cosideratio. I order to solve this problem oe has first of all to choose some referece poit x 0 = (x 01, x 02,, x 0 ), Hellwig called it the patter of ecoomic developmet. Next, for each object oe has to calculate its level of developmet accordig to the followig formula: ci d 1, i = 1,2,, N, i c 0 where N is the umber of coutries evaluated with respect to their status of developmet, ad the quatities c i ad c 0 are defied as follows: N 1 with c c i. N i1 c i ( xij j1 x 0 j ) 2 1/ 2 N 1 2 c 0 c 2 ( c i c) N i1 Vector x i = (x i1, x i2,, x i ) cotais the features characterig the evaluated coutries ad the referece vector x 0 = (x 01, x 02,, x 0 ) has bee called the patter of ecoomic developmet., 1/ 2,

8 85 th birthday of Profesor Zdzisław H. Hellwig 61 ŚLĄSKI 5. Measure of stochastic depedece The other sigificat achievemet of Prof. Hellwig is the measure of stochastic depedece. For the case of two-dimesioal radom vector (X, Y) this measure has bee defied as follows: 1/ 2 d ( 1 mi[ f ( x, y), f1 ( x) f2( y) dxdy). For the discrete case this measure has bee defied by the followig formula: r s 1 mi( p, ) ij piqs i1 j1 d 1 1 (mi( r, s)) 1/ 2 Both of them were further ivestigated i a umber of papers.. 6. Distace variable I the book o stochastic approximatio published i 1965 Z. Hellwig itroduced a ew statistical cocept, ad amely, the cocept of distace variable [Hellwig 1965, 1969]. It has bee defied as follows m m m Let X ( X, X,..., X ), X ( X, X,..., ),..., X X, X, X ( 1 2 m..., X m } be a simple radom sample from the distributio give by cdf F(x 1,, x ) or by the desity fuctio f(x 1,, x ). The distace radom variable, deoted by symbol C m,, is defied as follows: where C mi( Y, Y,..., Y 1 2 m,, m 1/ 2 0 j 2 Y ( ) j X i X i j = 1, 2,, m. i1 ),

9 ŚLĄSKI 62 Walety Ostasiewicz Ituitively, variable C m, meas the shortest distace betwee a m radom vector X ad a set of radom vectors X 2, X,..., X. The geeral expressio for the cumulative distributio fuctio foud by B. Kopociński is followig where: F Cm m ( c) 1 (1 (,,...,, )),...,, V x x x c dx dx 1 2 R with V x... x, c) f ( x u, x u,..., x u ) du... du ( A where: A {( u1..., u ) u1 u2... u c}. The limit distributio, whe m, is followig F C K ( c) ( c) 1 e f ( x, x,..., x ) dx... dx, R K ( c) / 2 c / ( / 2 1). G. Trybuś reports the explicit exact formulae for these distributios for some populatios i his moograph (Zmiea losowa dystasowa. Teoria i zastosowaia, Prace Naukowe Akademii Ekoomiczej r 173, AE, Wrocław 1981), where there are refereces to the origial works of B. Kopociński ad W. Dziubdziela. 7. Excerpt from UNESCO paper The well kow taxoomic method developed by Z. Hellwig has bee first published by UNESCO. The fragmet of the paper is give below.

10 85 th birthday of Profesor Zdzisław H. Hellwig 63 ŚLĄSKI

11 ŚLĄSKI 64 Walety Ostasiewicz The distace matrix is followig.

12 85 th birthday of Profesor Zdzisław H. Hellwig 65 ŚLĄSKI

13 ŚLĄSKI 66 Walety Ostasiewicz Selected works by Z. Hellwig Hellwig Z., Problem optymalego wyboru predykat, Przegląd Statystyczy 1968, No Hellwig Z., Aproksymacja. stochastycza, PWE, Warszawa Hellwig Z., O the measuremet of stochastical depedece, Zastosowaia Matematyki 1969, Vol. 10, pp

14 85 th birthday of Profesor Zdzisław H. Hellwig 67 ŚLĄSKI Hellwig Z., Efekt katalizy jego wykrywaie i usuwaie, Przegląd Statystyczy 1977, No. 2, pp Hellwig Z., Przechodość skorelowaia między zmieymi losowymi i płyące stąd wioski ekoometrycze, Przegląd Statystyczy 1976, No. 1, pp Hellwig Z., Regresja liiowa i jej zastosowaie w ekoomii, PWE, Warszawa Hellwig Z., Liear Regressio ad Its Applicatio to Ecoomics, Pergamo Press, Oxford Hellwig Z., Przyczyek do teorii regresji, Zeszyty Naukowe WSE, Wrocław 1961.