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2021 | OriginalPaper | Chapter

3. Sampling Designs Based on Order Statistics of an Auxiliary Variable

Author : Janusz L. Wywiał

Published in: Sampling Designs Dependent on Sample Parameters of Auxiliary Variables

Publisher: Springer Berlin Heidelberg

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Abstract

In this chapter, the properties of sampling designs proportional to the sample order statistic (quantile) as well as functions of two- or three-order statistics are considered in detail. Conditional sampling designs are also taken into account and exact expressions for inclusion probabilities are presented. The sampling schemes for these sampling designs are also proposed, some of which are generalized to the case of continuous-type sampling designs in the last chapter of the book.

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Literature
go back to reference David, H. A., & Nagaraja, H. N. (2003). Order Statistics. Hoboken: Wiley David, H. A., & Nagaraja, H. N. (2003). Order Statistics. Hoboken: Wiley
go back to reference Singh, P., Srivastava, & A. K. (1980). Sampling schemes providing unbiased regression estimators. Biometrika, 67(1), 205–209. Singh, P., Srivastava, & A. K. (1980). Sampling schemes providing unbiased regression estimators. Biometrika, 67(1), 205–209.
go back to reference Tillé, Y.(1998). Estimation in surveys using conditional inclusion probabilities: simple random sampling. International Statistical Review, 66(3), 303–322. Tillé, Y.(1998). Estimation in surveys using conditional inclusion probabilities: simple random sampling. International Statistical Review, 66(3), 303–322.
go back to reference Wilks, S. S. (1962). Mathematical Statistics. New York, London: Wiley.MATH Wilks, S. S. (1962). Mathematical Statistics. New York, London: Wiley.MATH
go back to reference WywiałJ, L. (2003). On conditional sampling strategies. Statistical Papers, 44(3), 397–419. WywiałJ, L. (2003). On conditional sampling strategies. Statistical Papers, 44(3), 397–419.
go back to reference Wywiał, J. L. (2008). Sampling design proportional to order statistic of auxiliary variable. Statistical Papers, 49(2), 277–289.MathSciNetCrossRef Wywiał, J. L. (2008). Sampling design proportional to order statistic of auxiliary variable. Statistical Papers, 49(2), 277–289.MathSciNetCrossRef
go back to reference Wywiał, J. L. (2009a). Performing quantiles in regression sampling strategy. Model Assisted Statistics and Applications, 4(2), 131–142.MathSciNetCrossRef Wywiał, J. L. (2009a). Performing quantiles in regression sampling strategy. Model Assisted Statistics and Applications, 4(2), 131–142.MathSciNetCrossRef
go back to reference Wywiał, J. (2009b). Sampling design proportional to positive function of order statistics of auxiliary variable. Studia Ekonomiczne-Zeszyty Naukowe, 53, 35–60. Wywiał, J. (2009b). Sampling design proportional to positive function of order statistics of auxiliary variable. Studia Ekonomiczne-Zeszyty Naukowe, 53, 35–60.
go back to reference WywiałJ, L. (2011). Sampling designs proportionate to sum of two order statistics of auxiliary variables. Statistics in Transition—New Series, 14(2), 231–248. WywiałJ, L. (2011). Sampling designs proportionate to sum of two order statistics of auxiliary variables. Statistics in Transition—New Series, 14(2), 231–248.
go back to reference Wywiał, J. L. (2016). Contributions to Testing Statistical Hypotheses in Auditing. Warsaw: PWN. Wywiał, J. L. (2016). Contributions to Testing Statistical Hypotheses in Auditing. Warsaw: PWN.
Metadata
Title
Sampling Designs Based on Order Statistics of an Auxiliary Variable
Author
Janusz L. Wywiał
Copyright Year
2021
Publisher
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-662-63413-4_3

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