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Multi-Domain Neyman-Tchuprov Optimal Allocation

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  • Wesołowski Jacek

    (Statistics Poland and Warsaw University of Technology, Warsaw, Poland .)

Abstract

The eigenproblem solution of the multi-domain efficient allocation is identified as a direct generalization of the classical Neyman-Tchuprov optimal allocation in stratified SRSWOR. This is achieved through analysis of eigenvalues and eigenvectors of a suitable population-based matrix D. Such a solution is an analytical companion to NLP approaches, which are often used in applications, see, e.g. Choudhry, Rao and Hidiroglou (2012). In this paper we are interested rather in the structure of the optimal allocation vector and relative variance than in such purely numerical tools (although the eigenproblem solution provides also numerical solutions, see, e.g. Wesołowski and Wieczorkowski (2017)). The domain-wise optimal allocation and the respective optimal variance of the estimator are determined by the unique direction (defined in terms of the positive eigenvector of matrix D) in the space ℝI, where I is the number of domains in the population.

Suggested Citation

  • Wesołowski Jacek, 2019. "Multi-Domain Neyman-Tchuprov Optimal Allocation," Statistics in Transition New Series, Polish Statistical Association, vol. 20(4), pages 1-12, December.
    • Handle: RePEc:vrs:stintr:v:20:y:2019:i:4:p:1-12:n:3
    DOI: 10.21307/stattrans-2019-031
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    References listed on IDEAS

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    1. Wright, Tommy, 2017. "Exact optimal sample allocation: More efficient than Neyman," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 50-57.
    2. Jacek Wesołowski & Robert Wieczorkowski, 2017. "An eigenproblem approach to optimal equal-precision sample allocation in subpopulations," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(5), pages 2212-2231, March.
    3. Siegfried Gabler & Matthias Ganninger & Ralf Münnich, 2012. "Optimal allocation of the sample size to strata under box constraints," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(2), pages 151-161, February.
    4. Kozak, Marcin & Zielinski, Andrzej & Singh, Sarjinder, 2008. "Stratified two-stage sampling in domains: Sample allocation between domains, strata, and sampling stages," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 970-974, June.
    5. Friedrich, Ulf & Münnich, Ralf & de Vries, Sven & Wagner, Matthias, 2015. "Fast integer-valued algorithms for optimal allocations under constraints in stratified sampling," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 1-12.
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