On the performance of subset selection rules under normality

From k normal populations N( θ 1, σ 1 2),…,N( θ k , σ k 2), where the means θ 1,…,θ k∈ R are unknown, and the variances σ 1 2,…, σ k 2>0 are known, independent random samples of sizes n 1,…, n k , respectively, are drawn. Based on these observations, a non-empty subset of these k populations of p...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2002-04, Vol.103 (1), p.101-115
Main Authors: Gupta, Shanti S., Miescke, Klaus J.
Format: Article
Language:English
Subjects:
Admissible subset selection rules
Bayes selection rules
Distribution theory
Exact sciences and technology
Independent normal populations
Mathematics
Parametric inference
Probability and statistics
Sciences and techniques of general use
Statistics
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Summary:From k normal populations N( θ 1, σ 1 2),…,N( θ k , σ k 2), where the means θ 1,…,θ k∈ R are unknown, and the variances σ 1 2,…, σ k 2>0 are known, independent random samples of sizes n 1,…, n k , respectively, are drawn. Based on these observations, a non-empty subset of these k populations of preferably small size has to be selected, which contains the population with the largest mean with a probability of at least P ∗ at every parameter configuration. Several subset selection rules which have been proposed in the literature are compared with Bayes selection rules for normal priors under two natural type of loss functions. Two new subset selection rules are considered.
ISSN:0378-3758
1873-1171
DOI:10.1016/S0378-3758(01)00214-2