A computational approach to the Kiefer-Weiss problem for sampling from a Bernoulli population

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Sequential Analysis-Design Methods and Applications Pub Date : 2021-10-10 DOI:10.1080/07474946.2022.2070212

A. Novikov, Andrei Novikov, Fahil Farkhshatov

引用次数: 5

Abstract

Abstract We present a computational approach to the solution of the Kiefer-Weiss problem. Algorithms for construction of the optimal sampling plans and evaluation of their performance are proposed. In the particular case of Bernoulli observations, the proposed algorithms are implemented in the form of R program code. Using the developed computer program, we numerically compare the optimal tests with the respective sequential probability ratio test (SPRT) and the fixed sample size test for a wide range of hypothesized values and type I and type II errors. The results are compared with those of D. Freeman and L. Weiss (Journal of the American Statistical Association, 59, 1964). The R source code for the algorithms of construction of optimal sampling plans and evaluation of their characteristics is available at https://github.com/tosinabase/Kiefer-Weiss.

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从伯努利种群中抽样的Kiefer-Weiss问题的计算方法

摘要我们提出了一种求解Kiefer-Weiss问题的计算方法。提出了最优抽样计划的构造算法及其性能评估算法。在伯努利观测的特殊情况下，所提出的算法以R程序代码的形式实现。使用开发的计算机程序，我们对各种假设值以及I型和II型误差的最优检验与相应的序列概率比检验（SPRT）和固定样本量检验进行了数值比较。将结果与D.Freeman和L.Weiss（《美国统计协会杂志》，1964年第59期）的结果进行了比较。用于构建最佳采样计划及其特性评估的算法的R源代码可在https://github.com/tosinabase/Kiefer-Weiss.

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Sequential Analysis-Design Methods and Applications STATISTICS & PROBABILITY-

CiteScore

1.40

自引率

12.50%

发文量

期刊介绍： The purpose of Sequential Analysis is to contribute to theoretical and applied aspects of sequential methodologies in all areas of statistical science. Published papers highlight the development of new and important sequential approaches. Interdisciplinary articles that emphasize the methodology of practical value to applied researchers and statistical consultants are highly encouraged. Papers that cover contemporary areas of applications including animal abundance, bioequivalence, communication science, computer simulations, data mining, directional data, disease mapping, environmental sampling, genome, imaging, microarrays, networking, parallel processing, pest management, sonar detection, spatial statistics, tracking, and engineering are deemed especially important. Of particular value are expository review articles that critically synthesize broad-based statistical issues. Papers on case-studies are also considered. All papers are refereed.