A restricted subset selection procedure for selecting the largest normal mean under heteroscedasticity

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Sequential Analysis-Design Methods and Applications Pub Date : 2023-01-02 DOI:10.1080/07474946.2022.2159042

Elena M. Buzaianu, Pinyuen Chen, Lifang Hsu

引用次数: 0

Abstract

Abstract This article considers the goal of selecting the population with the largest mean among k normal populations when variances are not known. We propose a Stein-type two-sample procedure, denoted by for selecting a nonempty random-size subset of size at most m ( ) that contains the population associated with the largest mean, with a guaranteed minimum probability whenever the distance between the largest mean and the second largest mean is at least where m, and are specified in advance of the experiment. The probability of a correct selection and the expected subset size of are derived. Critical values/procedure parameters that are required for certain k, m, and are obtained by solving simultaneous integral equations and are presented in tables.

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异方差条件下选择最大正态均值的一个受限子集选择过程

摘要本文考虑在方差未知的情况下，在k个正态总体中选择平均值最大的总体的目标。我们提出了一种Stein型双样本程序，表示为选择一个大小最大为m（）的非空随机大小子集，该子集包含与最大平均值相关的总体，只要最大平均值和第二大平均值之间的距离至少在m处，就有保证的最小概率，并且是在实验之前指定的。导出了正确选择的概率和预期的子集大小。某些k、m所需的临界值/程序参数，通过求解联立积分方程获得，并在表中列出。

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.