递归内曼分配的最优性

IF 1.6 4区数学 Q2 SOCIAL SCIENCES, MATHEMATICAL METHODS

Journal of Survey Statistics and Methodology Pub Date : 2021-05-30 DOI:10.1093/jssam/smab018

J. Wesołowski, R. Wieczorkowski, Wojciech W'ojciak

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引用次数: 4

摘要

在样本层大小的上限下，我们导出了一般分层方案中最优样本分配的公式。这种一般方案包括地层内的SRSWOR作为特例。该解是根据V分配给出的，其中V是所有阶层的集合。我们使用V分配给出了流行的递归Neyman算法rNa的最优性的形式证明。我们还提出了Stenger和Gabler算法的最优性的快速证明，SGa，以及我们提出的修改，coma。最后，我们比较了rNa、SGa和昏迷的运行时间。这些算法的现成R实现可在CRAN存储库中获得，网址为https://cran.r-project.org/web/packages/stratallo.

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Optimality of the Recursive Neyman Allocation

We derive a formula for the optimal sample allocation in a general stratified scheme under upper bounds on the sample strata sizes. Such a general scheme includes SRSWOR within strata as a special case. The solution is given in terms of V allocation with V being the set of take-all strata. We use V allocation to give a formal proof of optimality of the popular recursive Neyman algorithm, rNa. We also propose a quick proof of optimality of the algorithm of Stenger and Gabler, SGa, as well as of our proposed modification, coma. Finally, we compare running times of rNa, SGa, and coma. Ready-to-use R-implementations of these algorithms are available on CRAN repository at https://cran.r-project.org/web/packages/stratallo.

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来源期刊

Journal of Survey Statistics and Methodology Multiple-

CiteScore

4.30

自引率

9.50%

发文量

期刊介绍： The Journal of Survey Statistics and Methodology, sponsored by AAPOR and the American Statistical Association, began publishing in 2013. Its objective is to publish cutting edge scholarly articles on statistical and methodological issues for sample surveys, censuses, administrative record systems, and other related data. It aims to be the flagship journal for research on survey statistics and methodology. Topics of interest include survey sample design, statistical inference, nonresponse, measurement error, the effects of modes of data collection, paradata and responsive survey design, combining data from multiple sources, record linkage, disclosure limitation, and other issues in survey statistics and methodology. The journal publishes both theoretical and applied papers, provided the theory is motivated by an important applied problem and the applied papers report on research that contributes generalizable knowledge to the field. Review papers are also welcomed. Papers on a broad range of surveys are encouraged, including (but not limited to) surveys concerning business, economics, marketing research, social science, environment, epidemiology, biostatistics and official statistics. The journal has three sections. The Survey Statistics section presents papers on innovative sampling procedures, imputation, weighting, measures of uncertainty, small area inference, new methods of analysis, and other statistical issues related to surveys. The Survey Methodology section presents papers that focus on methodological research, including methodological experiments, methods of data collection and use of paradata. The Applications section contains papers involving innovative applications of methods and providing practical contributions and guidance, and/or significant new findings.