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## Studia Ekonomiczne / Akademia Ekonomiczna w Katowicach

2009 | nr 53 Metody wnioskowania statystycznego w badaniach ekonomicznych | 35--59
Tytuł artykułu

### Sampling Design Proportional to Positive Function of Order Statistics of Auxiliary Variable

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
The sampling design proportional to some positive function of an auxiliary variable is considered. Its characteristics are derived on the basis of well known combinatoric definitions and theorems. For instance, it is well known the sampling design proportional to the sample mean, see Lahiri (1951). The sampling design proportional to the value of an order statistics of an auxiliary variable was prepared by Wywiał (2004, 2007). In this paper that sampling design is generalized in the following way. The sampling design proportional to the positive function of order statistics of the auxiliary variable is defined and its basic properties are considered. Its inclusion probabilities are derived. This let to use the Horvitz-Thompson statistic to estimation population mean value of an variable under study. The sampling scheme implementing the sampling design is proposed, too. Particular cases of the proposed sampling design are as follows. The sampling design proportional to the sample second L-statistics of the auxiliary variable. Sampling design proportional to the sample range of the auxiliary variable. It is useful to construction sampling strategy using estimators of the regression coefficients based on order statistics of the auxiliary variable. (original abstract)
Słowa kluczowe
Rocznik
Strony
35--59
Opis fizyczny
Twórcy
autor
• The Karol Adamiecki University of Economics in Katowice, Poland
Bibliografia
• Das A.K., Tripathi T.P. (1980): Sampling Strategies for Population Mean When the Coefficient of Variation ot Auxiliary Characer is Known. "Sankhya", Vol. C42.
• Elamir E.A.H., Seheult A.H. (2003): Trimmed L-moments. "Computational Statistics and Data Analysis", Vol. 43, pp. 299-314.
• Fisz M. (1963): Probability Theory and Mathematical Statistics. Wiley and Sons Inc., New York.
• Guenther W. (1975): The Inverse Hypergeometric - a Useful Model. "Statistica Neerlandica", Vol. 29, pp. 129-144.
• Hogg R.V., Craig A.T. (1970): Introduction to Mathematical Statistics. 3rd edition. MacMillian, New York.
• Horvitz D.G., Thompson D.J. (1952): A Generalization ot the Sampling without Replacement from Finite Universe. "Journal of the American Statistical Association", Vol. 47. pp. 663-685.
• Johnson N., Kotz S. (1969): Distributions in Statlstics: Discrete Distributions. Houghton Mifflin Company, Boston.
• Lahiri G.W. (1951): A Method for Sample Selection Provlding Unbiased Ratio Estimator. "Bulletin of the International Statistical Institute", Vol. 33, pp. 133-140.
• Patil G.G., Joshi S.W. (1968): A Dictionary and Bibliography of Discrete Distributions. Hafner, New York.
• Sillito G.P. (1969): Derivation of Approximations to the Inverse Distribution Function of a Continuous Univariate Population from the Order Statistics of a Sample. "Biometrika", Vol. 56, pp. 641-650.
• Singh P., Srivastava A.K. (1980): Sampling Schemes Providing Unbiased Regression Estimators. "Biometrika", Vol. 67, 1, pp. 205-209.
• Srivastava S.K., Jhajj H.S. (1981): A Class ot Estimators of the Population Mean in Survey Sampling Using Auxiliary Intormation. "Biometrika", Vol. 68.
• Tille Y. (1998): Estimation in Surveys Using Conditional Inlusion Probabilities: Simple Random Sampling. "International Statistical Review", Vol. '66. 3, pp. 303-322.
• Wilks S.S. (1962): Mathematical Statistics. John Wiley and Sons, Inc., New York-London.
• Wywiał J. (1999): Sampling Designs Dependent on the Sample Generalized Variance of Auxiliary Va- riables. "Journal of the Indian Statistical Association", Vol. 37, pp. 73-87.
• Wywiał J. (2000): On Precision of Horvitz-Thompson Strategies. "Statistics in Transition", Vol. 4. No. 5, pp. 779-798.
• Wywiał J. (2003). Some Contributions to Multivariate Methods in Survey Sampling. Karol Adamiecki University of Economics, Katowice.
• Wywiał J. (2003a): On Conditional Sampling Strategies. "Statistical Papers", Vol. 44,3, pp. 397-419.
• Wywiał J. (2004): Quantile Regression Sampling Strategy. In: Metoda Reprezentacyjna w Badaniach Ekonomiczno-Społecznych. Red. J. Wywiał. AE, Katowice, pp. 32-42.
• Wywiał J. (2007): Sampling Design Proportional to Order Statistic of Auxiliary Variable. "Statistical Papers" April, Vol. 49, No. 2, pp. 277-289.
• Wywiał J. (2007a): Simulation Analysls of Accuracy Estimation of Population Mean on the Basis of Strategy Dependent on Sampling Design Proportionate to the Order Statistic of an Auxiliary Variable. "Statistics in Transition-New series", Vol. 8, No. 1, pp. 125-137.
Typ dokumentu
Bibliografia
Identyfikatory
bwmeta1.element.ekon-element-000171223629

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