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2003 | 226
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Some Contributions to Multivariate Methods in Survey Sampling

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Języki publikacji
EN
Abstrakty
W praktyce badań reprezentacyjnych zwykle mamy do czynienia z problemem wnioskowania o wielu parametrach analizowanych cech populacji. Rzadko celem takiego badania jest ocena wartości jednego parametru, chociaż temu właśnie przypadkowi jest głównie poświęcana większość prac z metody reprezentacyjnej. Bynajmniej nie oznacza to, iż te prace mijają się z praktycznymi potrzebami badań statystycznych, ponieważ otrzymywane wyniki dotyczące wnioskowania o pojedynczym parametrze jednowymiarowej cechy można w wielu zagadnieniach bezpośrednio uogólnić na przypadek wielowymiarowy. W tej dziedzinie są jednak problemy jednoczesnego wnioskowania o wielu parametrach, które wymagają szczególnego podejścia. Należą do nich problem sposobu oceny dokładności estymacji wektora parametrów oraz interpretacja używanych do tego celu wskaźników. Kluczowe znaczenie ma także usystematyzowanie podstawowych wiadomości pozwalających na porównywanie dokładności estymatorów wektorowych. Następna kwestia dotyczy optymalizacji badań próbkowych, a zwłaszcza optymalizacji rozmiarów prób złożonych, gdy występują ograniczone nakłady na badania reprezentacyjne oraz żądania spełnienia wymaganej dokładności oceny parametrów. W ogólności właśnie wymienionym problemom jest poświęcona niniejsza praca. Prezentowano w niej głównie zagadnienia dotyczące jednoczesnej estymacji wielu parametrów cech w populacji. Nacisk położono na prezentację wyników otrzymanych przez autora. W pracy ograniczono się głównie do analizy problemu estymacji wektora wartości średnich w populacji. Otrzymane na tym polu wyniki można jednak łatwo przenieść na zagadnienie oceny innych ważnych z punktu widzenia praktyki parametrów, takich jak suma wartości cechy w populacji, ilość elementów z cechą wyróżnioną w populacji, częstość względna występowania określonego zjawiska w populacji. W pierwszym rozdziale przedstawiono podstawowe definicje związane z rozkładami cech w populacji ustalonej, jak i w tzw. nadpopulacji. Podstawowe parametry rozkładu wektora znanych estymatorów Horvitza-Thompsona są prezentowane w drugim rozdziale. W trzecim rozdziale prezentowano podstawowe własności rozkładu wektora estymatorów z próby warstwowej. Podstawowe parametry rozkładu wektora średnich z próby grupowej prezentowano w rozdziale czwartym. Rozdział piąty dotyczy estymacji wektora średnich w populacji na podstawie wektora średnich z próby dwustopniowej. Szósty rozdział jest poświęcony wektorowym estymatorom różnicowym i regresyjnym. (abstrakt skrócony)
EN
The book can be treated as a set of contributions to the estimation of a vector of the averages of variables in a finite population. The methods presented are not only a simple generalisation of the well known problems on a multidimensional case but a lot of them can be treated as original ones. Particularly, several sampling strategies dependent on auxiliary variables arc proposed. The problems of optimising a sample size are considered in detail for stratified and two-stage sampling designs in the case when more than one average in a population is estimated. The well known discrimination and clustering methods and their modifications are used for optimal stratification or clustering of a fixed population. Solutions obtained here can be useful in optimisation of estimation on the basis of a double sample. The book presents some contributions to interpretations of the following measures of accuracy of vector estimators: the generalised variance, the mean radius and spectral radius defined as a determinant, the trace and the maximal eigenvalue of the variance-covariance matrix, respectively. Some definitions and theorems, known in a one-dimensional case are extended to the vector estimation case. They let us compare the accuracy of vector estimators. The properties of sampling designs and sampling schemes depend on the parameters of auxiliary variables like the sample generalised variance, the squared difference between the sample mean and the population mean are considered. The approximate expressions of the variance of the Horovitz-Thompson estimator of the mean value are derived for these sampling designs. The unbiased estimators of the generalised variance are found in the cases when the simple sample is drawn with as well as without replacement. (fragment of the original abstract)
Rocznik
Strony
226
Opis fizyczny
Twórcy
  • The Karol Adamiecki University of Economics in Katowice, Poland
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  • Wywiał J. (2002a): On estimation of population average on the basis of cluster sample. In: Classification, Clustering, and Dala Analysis. Eds. K. Jajuga. A. Sokołowski, H.H. Bock. Springer Berlin, Heidelberg, New York, Barcelona, Hong Kong, London, Milan. Paris, Tokyo, 2002, pp. 271-277.
  • Wywiał J. (2002b). On the accuracy of mean estimation on the basis of two-phase sampling for stratification. W: Statystyka regionalna w służbie samorządu lokalnego i biznesu pod. red. Jana Paradysza. Akademia Ekonomiczna w Poznaniu, Internetowa Oficyna Wydawnicza, Centrum Statystyki Regionalnej, Poznań.
  • Wywiał J., Kończak G. (1994): On location of sample in strata minimizing spectral radius of variance-covariance matrix, (in Polish). In: Proceedings of the XI Conference devoted to. Professor Zbigniew Pawłowski. Trzemieśnia 24-26 III. Akademia Ekonomiczna w Krakowie, s. 85-92.
  • Yates F., Grundy P.M. (1953); Selection without replacement from within strata with probability proportional! to size. Journal of the Royal Statistical Society", vol. B15, pp. 235-261.
  • Yates F. (1960): Sampling methods for censuses and surveys. Griffin & Company Ltd., London.
  • Zasępa R. (1972): Survey Sampling (in Polish). PWE, Warszawa.
  • Zieliński R. (1979). Generators of random pseudovalues (in Polish). WNT, Warszawa.
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Bibliografia
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