Selection from multivariate normal populations
Selection from multivariate normal populations
复制标题
从多变量正态总体中选择
DOI：
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发表时间：
1966
期刊：
影响因子：
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通讯作者：
M. H. Rizvi
中科院分区：
文献类型：
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作者：
K. Alam;M. H. Rizvi
**摘要**
本文关注非中心卡方和非中心F总体的选择与排序问题，这些总体是依据其非中心性参数来定义的。我们感兴趣的是选出t个最大的总体以及包含这t个最大总体的一个子集，为此给出了两种方法，分别命名为R1和R2。要求使用这些方法进行正确选择的概率至少要和任何给定的小于1的数P*一样大。我们将此称为“P*条件”。问题的主要部分是确定参数空间中使正确选择概率最小的最不利配置。最小值的表达式决定了满足P*条件所需的最小样本量。针对R1和R2，得到了最不利配置以及正确选择概率最小值的相应表达式。
SummaryThis paper is concerned with the problems of selection and ranking of non-central chi-squared and non-centralF populations, defined in terms of their non-centrality parameters. We are interested in selecting thet largest of the populations and a subset containing thet largest for which two procedures, namedR2 andR2 are given. It is required that the probability of a correct selection using these procedures should be at least as large as any given number P*< 1. We call this the “P* condition”. The main part of the problem is to determine the least favorable configurations of the parameter space for which the probability of a correct selection is minimum. The expression for the minimum value determines the smallest sample size needed to satisfy theP* condition. The least favorable configurations and the corresponding expressions for the minimum of the probability of a correct selection are obtained forR1 andR2.