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2003 | 226
Tytuł artykułu

Some Contributions to Multivariate Methods in Survey Sampling

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Warianty tytułu
Języki publikacji
EN
Abstrakty
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)
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)
Rocznik
Strony
226
Opis fizyczny
Twórcy
  • The Karol Adamiecki University of Economics in Katowice, Poland
Bibliografia
  • Anderson T.W. (1958): Аn Introduction to Multivariate Statistical Analysis. John Wiley & Sons, New York.
  • Anderson D.W., Kish L., Cornell R.G. (1980): On stratification, grouping and matching. Scandinavian Journal of Statistics, vol. 7, pp. 61 - 66.
  • Arwanitis L.G., Afonia B. (1971): Use of generalized variance and the gradient projection method in multivariate stratified sampling. Biometrics.. vol. 27, pp. 119-127.
  • Beardwood J., Halton J.H., Hammersley J.M. (1959): The shortest path through many points. Proceedings of Cambridge Phil. Soc., vol. 55.
  • Bethel J. (1989): Sample allocation in multivariate surveys. Survey Methodology, vol. 15, nr 1, pp. 47-57.
  • Bethleham, J.G. (1988); Reduction of nonresponse bias through regression estimation. Journal of Official Statistics, 4, pp.251 - 260.
  • Blythe J.R.H. (1945): The economics of sample size applied to the scaling of sowlongs. Biometrics Bulletin, vol. I, s. 67-70.
  • Borovkov A.A. (1984): Mathematical statistics. Estimation. Testing Hypothesis (in Russian). Nauka, Moscow.
  • Borsuk K. (1976): Multidimensional Analytical Geometry. PWN, Warszawa.
  • Bracha Cz. (1978): Estimation of linear regression parameters on the basis of sample drawn without replacement from finite population (in Polish). Przegląd Statystyczny, vol. 25.
  • Bracha Cz. (1982): Estimation of linear regression parameters on the basis of two-stage sample (in Polish). Przegląd Statystyczny, vol. 29.
  • Bracha Cz. (1983): Linear Regression in Survey Sampling (in Polish). Prace i Materiały Instytutu Cybernetyki i Zarządzania. SGPiS, Warszawa.
  • Bracha Cz. (1987): Using Auxiliary Information in Survey Sampling, (in Polish). ZBS-GUS i PAN, Warszawa.
  • Bracha Cz. (1991): Selected problems of stratifying sampling, (in Polish) Prace i Materiały Instytutu Cybernetyki i Zarządzania. Tom 20. SGPiS, Warszawa.
  • Bracha Cz. (1996): Teoretyczne podstawy metody reprezentacyjnej. PWN, Warszawa.
  • Cassel C.M.. Sarndal C.E., Wretman J.H. (1977): Foundation of inference in Survey Sampling. John Wiley & Sons, New York-London-Sydney-Toronto.
  • Chatterjee S. (1968): Multivariate stratified surveys. Journal of she American Statistical Association, vol. 63.
  • Cochran W.G. (1961): Comparison of methods for determining stratum boundaries. Bulletin of International Statistical Institute, vol. 38, No. 2. pp. 345-358.
  • Cochran W.G. (1963): Sampling Techniques. John Wiley & Sons, New York.
  • Cramer H. (1958): Mathematical Methods in Statistic, (in Polish) PWN, Warszawa.
  • Czerniak W. (1971): On independend sampling with replacement (in Polish). Biblioteka Wiadomości Statystycznych. Tom 15, pp. 40-86.
  • Dalenius T. (1950): The problem of optimum stratification. Journal of the American Statistical Association, vol. 54, pp. 88 - 101.
  • Dalenius T. (1953): The multivariate sampling problem. Scandiiiavisk Aktuarietidskrift, vol. 36, pp. 92-102.
  • Dalenius T. (1957): Sampling in Sweden. Contribution to Methods and Theories of Sample Survey Practice. Almqvist & Wiksells, Stockholm.
  • Dalenius Т., Gurney M. (1951): The problem of optimum stratification II. Scandinavisk Aktuarietidskrift, vol. 34, pp. 133-148.
  • Dalenius Т., Hodges J.L.Jr. (1959): Minimum variance stratification. Journal of the American Statistical Association, vol. 54, pp. 88-101.
  • Dayal S. (1985): Allocation of sample using values of auxiliary characteristic. Journal of Statistical Planning and Inference, vol. 11, pp. 321-328.
  • Demidowicz B.P., Maron I.A. (1965): Numerical Methods. Vol. I. (in Polish) PWN, Warszawa.
  • Dcville СМ., Sarndal C.E., (1992). Calibration estimators in survey sampling. Journal of the American Statistical Association, vol. 87, nr 418, pp. 376-382.
  • Donoho D.L., Gąsko M. (1992): Breakdown Properties of Location Estimate Based on Halspace Depth and Projected Outlyingness. Annals of Statistics 20, pp.1803- 1827.
  • Efron В., Tibshirani R.J. (1993). An Introduction to the Bootstrap. Chapman & Hall, New York, London.
  • Everitt B.S. (1998): The Cambridge Dictionary of Statistics. Cambridge University Press, Cambridge.
  • Fisz M. (1963): Probability Theory and Mathematical Statistics. Wiley, New York.
  • Fisz M. (1967): Introduction 10 Probability and Mathematical Statistics (in Polish). PWN, Warszawa.
  • Flachsmeyer J. (1977): Combinatorics (in Polish). PWN, Warszawa.
  • Gamrot W., Wywiał J. (2002). Comparison of the accuracy of some two-stage sampling schemes by means of computer simulation. Zeszytv Naukowe, no. 21, Akademia Ekonomiczna w Katowicach, p. 11-28.
  • Geary R.С. (1949): Sampling methods applied to Irish agricultural statistics. Technical Series.
  • Ghosh J.K. (1963): A game theory approach to the problem of optimum allocation in stratified sampling with multiple characters. Calcutta Statistical Association Bulletin, vol. 12. pp. 4-12.
  • Ghosh S.P. (1958): A note on stratified random sampling with multiple characters. Calcutta Statistical Association Bulletin, vol. 8, pp. 81-90.
  • Godambe V.P., Joshi V.M. (1965): Admissibility and Bayes estimation in sampling finite populations I. Annals of Mathematical Statistics, vol. 36, pp. 1707-1722.
  • Greń J. (1963): Localization of sample in the case of multiparameter stratified sampling (in Polish). Przegląd Statystyczny, vol. 10, pp. 291-302.
  • Greń J. (1964): On some methods of localization of sample in the case of multiparameter stratified sampling(in Polish). Przegląd Statystyczny, vol. 11, pp. 361-369.
  • Greń J, (I966): On application of non-linear programming to survey sampling (in Polish). Przegląd Statystyczny, vol. 13, pp. 203-217.
  • Greń J. (1969): Multidimensional regression estimator of mean values (in Polish). Przegląd Statystyczny, vol. 16.
  • Greń J. (1970): Multidimensional regression estimator of mean values in finite population (in Polish). Przegląd Statystyczny, vol. 17, pp. 73-78.
  • Greń J., Koźniewska I. (1964): Solution to some recurrence equation connected with two-parameter stratified sampling (in Polish). Przegląd Statystyczny, vol. 11, pp. 169-176.
  • Hartigan J.A. (1975). Clustering Algorithms. New York. J. Wiley.
  • Hartley H.O. (1965): Multiple purpose optimum allocation in stratifed sampling. Proceedings of the American Statistical Association, Social Statistics Section, pp. 258-261.
  • Hartley H.О., Rao J.N.K. (1969): A new estimation theory for sample surveys II. In: New Developments in Survey Sampling. Edited by N.L. Johnson and H. Smith. Wiley-Interscience, New York, pp. 147-169.
  • Hastings C. (1955). Approximation for digital computations. Princenton University Press, Princenton.
  • Herzel A. (1986): Sampling without replacement with unequal probabilities: sample designs with preassigned joint inclusion probabilities of any order. Met ran, vol. 44, no. 1-4, pp. 49-68.
  • Hess I., Sethi V.K., Balakrishnan Т.К. (1966): Stratification - a practical investigation. Journal of the American Statistical Association, vol. 61.
  • Horvitz D.G.. Thompson D.J. (1952): A generalization of sampling without replacement from finite universe. Journal of the American Statistical Association, vol. 47, pp. 663-685.
  • Huddleston H.F., Claypool P.L., Hocking R.R. (1970): Optimal sample allocation to strata using convex programming. Applied Statistics, vol. 19, pp. 273-278.
  • Hughes E.. Rao J.N.K. (1979): Some problems of optimal allocation in sample surveys involving inequality constrains. Communication in Statistics, vol. A8, pp. 1551-1571.
  • Iluisman M. (2000): Post-stratification to correct for nonresponse: classification of ZIP code areas. Compstat 2000. Proceedings in Computational Statistics, 14'h Symposium held in Utrecht, The Netherlands. Edited byJ.G, Bethlehaiu and P.G.M. van der Heijden, pp. 325-330.
  • Jaganathan R. (1965): The programming approach in multiple characters studies. Econometnca, vol. 33, pp. 236-237.
  • Jaganathan R. (1965a): A method for solving a nonlinear programming problem in sample surveys. "Econometrica". vol. 33, s. 841-846.
  • John S. (1969): On multivariate ratio and product estimators. Biometrika, vol. 56, pp. 533-537.
  • Jonin B.C., Jonina N.P., Zhuravlev N.M. (1978): Ispolsovanye protsedur op-timisatsyi pri klassifikatsy obyektov i faktorov. In: Ekonomika i statis-ticheskoye modyeli w prognozirovyi planirowanyi promyshlennogo proisvodstva. Nauka, Moskwa.
  • Joshi V.M. (1965): Admissibility and В ayes estimation in sampling finite populations II i III. Annals of Mathematical Statistics, vol. 36. pp. 1658-1670.
  • Joshi V.M. (1966): Admissibility and Bayes estimation in sampling finite populations IV. Annals of Mathematical Statistics, vol. 37, pp. 1658-1670.
  • Kish L. (1961): Efficient allocation of multipurpose sample. Econometrica, vol. 29, pp. 363-385.
  • Kish L. (1965): Survey sampling. John Wiley & Sons, Inc. New York-London-Sydney.
  • Kokan A.R. (1963): Optimum allocation in multivariate surveys. Journal of the Royal Statistical Society, vol. A 126, pp. 557-565.
  • Kokan A.R., Khan S. (1967): Optimum allocation in multivariate surveys: an analytical solution. Journal of the Royal Statistical Society, vol. В 29, pp. 135-125.
  • Konijn H.S. (1962): Regression analysis in sample surveys. Journal of the American Statistical Association, vol. 57.
  • Konijn H.S. (1973): Statistical theory of sample survey and analysis. North-Holland Publishing Company, Inc., Amsterdam-London, American Elsevier Publishing Company, Inc., New York.
  • Krzyśko M. (2000). Multidimensional Statistical Analysis (in Polish). Uniwersytet im Adama Mickiewicza, Poznań.
  • Kubik L.Т., Krupowicz A. (1982): Introduction To Probability and ITS Applications (in Polish). PWN, Warszawa.
  • Lahiri G.W. (1951): A method for sample selection providing unbiased ratio estimator. Bulletin of the International Statistical institute, vol. 33. pp. 133-140.
  • Lehman E,L. (1991): Theory of Estimation (in Polish). PWN, Warszawa.
  • Lipski W., Marek W. (1986): Combinatoric Analysis (in Polish). PWN, Warszawa.
  • Liu R. (1990): On a Notation of Data Depth Based Random Simplices. Annals of Statistics 18, pp. 405 - 414.
  • Lynch G.W. (1978): The choice of auxiliary variables in multivariate ratio and regression estimators. Proceedings of the Section on Survey Research Methods. American Statistical Association.
  • Mahalanobis P.C. (1944): On large scale sample surveys. Phil. Trans. Roy. Soc. London, vol. В 231, pp. 329-451.
  • Melaku A. S. (1987): L d-norm and other methods for sample allocation in multivariate stratified surveys. Computational Statistics & Data Analysis, vol. 5, pp. 415-423.
  • Mikhail N.N., Mir. M.A. (1981): Unbiased estimates of the generalized variance for finite population. Journal of the Indian Statistical Association, vol. 19, pp. 85-92.
  • Miller R., G. (1981). Simultaneous Statistical Inference. Springer Verlag, New York-Berlin-Heildelberg-London-Paris-Tokyo-Hong Kong-Barcelona.
  • Mukerjee R., Rao T.J. (1985): On a problem of allocation of sample size in stratified random sampling. Biometrical Journal, vol. 27, nr 3, pp. 327-331.
  • Murthy M.N. (1977): Sampling theory and practice. Statistical Publishing Society, Calcutta.
  • Neyman J. (1934): On two different aspects of the representative method: the method of stratified sampling and the method of purposive selection. Journal of the Royal Statistical Society, vol. 97, pp. 558-606.
  • Olkin I. (1958): Multivariate ratio estimation for finite populations. Biometrika, vol 45, pp. 154-165.
  • Ralston A. (1975): Introduction to Numerical Methods (in Polish). PWN: Warszawa.
  • Ramakrishnan M.K. (1975): Choice of an optimum sampling strategy I. Annals of Statistics, vol. 3, pp. 669-679.
  • Rao C.R. (1973). Linear Statistical Inference and Its Applications. John Wiley & Sons, Inc.. New York - London - Sydney - Toronto.
  • Rao C.R. (1982): Linear Models of Mathematical Statistics (in Polish). PWN. Warszawa.
  • Rao J.N.K. (1973): On double sampling for stratification and analytical surveys. Biometrika. vol. 60, nr 1. pp. 125-133.
  • Rao J.N.K. (1985): Conditional inference in survey sampling. Survey Methodology, Vol. 11,No. l.pp. 15-31.
  • Rao J.N.K.. A.J. Scott (1981). The analysis of categorical data from complex sample surveys: Chi-squared tests for goodness of fit and independence in two-way tables. Journal of The American Statistical Association, vol. 76, no. 374, pp. 221-230.
  • Rao T.V.H. (1962): An existence theorem in sampling theory. Sankhya, vol. A 24, pp. 327-330.
  • Royall R.M. (1970): On finite population sampling theory under certain linear regression models. Biometrika, vol. 57, pp. 377-387.
  • Sarndal C.E. (1976): On uniformly minimum variance estimation in finite populations. Annals of Statistics, vol. 4, pp. 993-997.
  • Sarndal C.E., B. Swensson, J. Wretman (1992): Model Assisted Survey Sampling. Springer Verlag, New York-Berlin-Heidelberg- London-Paris--Tokyo-Hong Kong- Barcelona-Budapest.
  • Schneeberg H., Pollot J.P. (1985): Optimum stratification with two variables. Statistical Papers, vol. 25, pp. 97 - 117.
  • Sen A.R. (1953): On the estimate of the variance in sampling with varying probabilities. Journal of the Indian Society of Agricultural Statistics. vo!5, pp. 119-127.
  • Sertling R.J. (1968): Approximately optimum stratification. Journal of the American Statistical Association, vol. 63.
  • Singh P., Srivastava A.K. (1980): Sampling schemes providing unbiased regresion estimators. Biometrika, vol. 67, pp. 205-209.
  • Singh R. (1971): Approximately optimal stratification on the auxiliary variable. Journal of the American Statistical Association, vol. 66, pp. 829-833.
  • Skibicki M. (2002). Maximization of measure of allowable sample sizes region in stratified sampling. In: Classification, Clustering, and Data Analysis. Eds. K. Jajuga, A. Sokolowski, H.H. Bock. Springer Berlin, Heidelberg. New York, Barcelona, Hong Kong, London, Milan, Paris. Tokyo. 2002, pp. 263-269.
  • Skibicki M. (2003). Optimatization of sample sizes drawn from strata on the basis of spectral radius of covariance matrix of means estimator vector. Statistics in Transition. In printing.
  • Skibicki M., J.Wywiał. (2001): On using clustering methods to stratification of population, (in Polish). Wiadomości Statystyczne, 2001, 8. pp. 4-11.
  • Skibicki M., Wywiał J. (2002). On optimal sample allocation in strata. W: Statystyka regionalna w służbie samorządu lokalnego i biznesu pod. red. Jana Paradysza. Akademia Ekonomiczna ir Poznaniu, Internetowa Oficyna Wydawnicza, Centrum Statystyki Regionalnej. Poznań.
  • Srikantan (1963): Problems in optimum allocation. Operational Research, vol. 11, pp. 265-273.
  • Theil H. (1979): Principles of Econometrics (in Polish). PWN, Warszawa.
  • Thomsen I. (1976): A comparison of approximately optimal stratification given proportional allocation with other method of stratification and allocation. Metrika, vol. 23, pp. 15 - 25.
  • Thompson M.E. (1997). Theory of Sample Surveys. Chapman & Hall, London - Weinhein - New York -Tokyo - Melbourne - Madras.
  • Tille Y. (1998): Estimation in surveys using conditional inclusion probabilities: simple random sampling. International Statistical Review, Vol. 66. No. 3, pp. 303 - 322.
  • Tille Y. (1999). Estimation in surveys using conditional inclusion probabilities: Complex Design. Survey Methodology, vol. 25, No 1. pp. 57-66.
  • Tripathi T.P. (1973): Double sampling for indusion probabilities and regression method of estimation. Journal of the Indian Statistical Association, vol. 10, pp.33-46.
  • Tripathi T.P. (1976): On double sampling for multivariate ratio and difference methods at estimation. Journal of the Indian Society of Agricultural Statistics, vol. 28, nr 1, pp. 33-54.
  • Tschuprow A.A. (1923): On the mathematical expectation of the moments of frequency distribution in the case of correlated observations. Metron. vol. 2. pp. 461-493 i s. 646-683.
  • Wagner W., Kobylińska M. (2000): On using depth measure in desribing statistic, (in Polish), In: Wyzwania i dylematy statystyki XXI wieku pod red. W. Ostasiewicza. Akademia Ekonomiczna we Wrocławiu.
  • Ward J.H. (1963): Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, vol. 58.
  • Williams W.H. (1962): The variance of an estimator with part-stratified weighing. Journal of the American Statistical Association, Vol. 57. pp. 622 - 627.
  • Wilks S.S. (1932): Certain generalization in the analysis of variance. Biometrika, vol. 24, pp. 471-494.
  • Wilks S.S. (1962): Mathematical statistics. John Wiley & Sons, Inc., New York-London.
  • Wywiał J. (1988): Estimation of vector of means on the basis of difference and regression estimators (in Polish). Przegląd Statystyczny, vol. 35, pp. 19-35.
  • Wywiał J. (1988a): Location of sample in strata minimizing spectral radius of variance-covariance matrix (in Polish). Prace Naukowe Akademii Ekonomicznej we Wrocławiu, nr 404 r pp. 195-200.
  • Wywiał J. (1989): On minimization of generalized variance of vector of means from stratified sample (in Polish). Wiadomości Statystyczne.. nr 11, pp. 23-24.
  • Wywiał J. (1990): On optimization of sizes of sample drawn from strata in the case of estimation of vector of mean values in finite population (in Polish). Zeszyty Naukowe Akademii Ekonomicznej w Katowicach, nr 117, pp. 19-32.
  • Wywiał J. (1991): Properties of cluster sample drawn from population clustered on the basis of auxiliary variable. Prace Naukowe Akademii Ekonomicznej we Wrocławiu, nr 559, pp. 107-112.
  • Wywiał J. (1991 a). On sampling design proportionate to sample mean of auxiliary variable (in Polish). Wiadomości Statystyczne, pp. 21-22.
  • Wywiał J. (1991b): On optimal stratification of fixed population on the basis of multidimensional auxiliary variable (in Polish). Badania Operacyjne i Decyzje 1991, no 2, pp.63-69.
  • Wywiał J. (1992). Survey Sampling in Economic Research (in Polish), Prace Naukowe Akademii Ekonomicznej w Katowicach.
  • Wywiał J. (I992a): On some coefficients measuring spread of multidimensional variable and generalization of Friedman-Rubin's clustering method of finite population (in Polish). Zeszyty Naukowe Akademii Ekonomicznej w Katowicach, nr 120, 129-149.
  • Wywiał J. (1993): Prediction of superpopulation average and clustering population on the basis of auxiliary variables, (in Polish). Przegląd Statystyczny, Vol. XL, zeszyt 3-4, pp. 303-308.
  • Wywiał J. (1995). Multidimensional Aspects in Survey Sampling (in Polish). Ossolineum, Warszawa-Wroclaw-Kraków.
  • Wywiał J. (1995a): On optimal stratification of population on the basis of auxiliary variables. Statistics in Transition. Vol. 2, No. 2, pp. 831-837.
  • Wywiał J. (1996): Unbiased estimators of generalized variance from simple random sample drawn without replacement from finite population. Journal of the Indian Statistical Association, vol. 34, pp. 125-129.
  • Wywiał J. (I996a): Generalization of the Ward method and its application to decomposition of regression relationship. Proceedings of 15" International Conference on Multivariate Statistical Analysis-MSA '96. University of Łódź., December 4-5, 1996, Łodz, pp. 59-75.
  • Wywiał J. (1996b): On space sampling. Statistics in Transition vol. 2 No. 7, pp. 1185-1191.
  • Wywiał J. (1996с): On two-phase sampling for stratification. Statistics in Transition. Vol. 2 No. 6, pp. 971-977.
  • Wywiał J. (1997): Decomposition of time series on the basis of modified grouping method of Ward. Acta Universitatis Lodzicnsis, Folia Oeconomica 141. p. 137-148.
  • Wywiał J. (1997a): Sampling Design proportional to the Sample Generalized Variance of Auxiliary Variables. Proceedings of 16th International Conference on Multivariate Statistical Analysis- MSA '97. Edited by Cz. Domanski and D. Parys. November 27-29 1997. Department of Statistical Methods, Institute of Econometrics and Statistics, University of Łódź, Polish Statistical Association. November 27-29. 1997r., pp. 129-143
  • Wywiał J. (1998): On stratification of a Population by means of Cluster Methods. Statistics in Transition vol. 3 no. 3, pp. 569-574.
  • Wywiał J. (1998a): Estimation of Population Average on the basis of Strata Formed by Means of Discrimination Functions. Statistics in Transition (Journal of the Polish Statistical Association) vol. 3, No. 5, pp. 903-912.
  • Wywiał J. (1999): Generalization of Singh and Srivastava's schemes providing unbiased regression estimators". Statistics in Transition vol. 2, No. 2, pp. 259-281.
  • Wywiał J. (1999a): "Sampling designs dependent on the sample generalized variance of auxiliary variables". Journal of the Indian Statistical Association. Vol. 37, pp. 73-87.
  • Wywiał J. (2000): "On precision of Horvitz-Thompson strategies. Statistics in Transition (Journal of the Polish Statistical Association) vol. 4, nr 5, pp. 779-798.
  • Wywiał J. (2000a). On optimal stratification of population in the case of estimation of mean vector (in Polish). Prace Naukowe Akademii Ekonomicznej we Wrocławiu nr 857. pp. 217-223.
  • Wywiał J. (2000b). On conditional estimation of population average on the basis of stratified population through clustering (he selected sample. Proceedings in Computational Statistics 14th Symposium held in Utrecht, the Netherlands, 2000. Short Communications and Posters. Edited by W. Jansen and J.G. Bethlehem. Statistics Netherlands.
  • Wywiał J. (2001). Stratification of population after sample selection. Statistics in Transition vol. 5, nr 2. 2001, pp. 327-348.
  • Wywiał J. (2001 a). Using of auxiliary variables to estimation of population parameters. Report from gram KBN 1II02B 008 !6, Akademia Ekonomiczna w Katowicach .
  • Wywiał J. (2001 b). On estimation of population mean in the case when non-respondents are present Prace Naukowe Akademii Ekonomicznej we Wrocławiu nr 906, Taksonomia 8, pp. 13-21.
  • Wywiał J. (2001c). Estimation of population mean on the basis of non-simple sample when non-response error is present. Statistics in Transition vol. 5. no. 3. pp. 443-450.
  • Wywiał J. (2002): On stratification of population on (he basis of auxiliary variable and the selected sample. Acta Universitatis, Folia Oeconomica 156, pp. 83-90.
  • 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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