Empirical Bayes Procedures for Selecting the Best Population with Multiple Criteria |
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Authors: | Wen-Tao Huang Yao-Tsung Lai |
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Institution: | (1) Institute of Statistical Science, Academia Sinica, Taipei, 115 Taiwan, R.O.C;(2) Graduate Institute of Mathematics, Tamkang University, Tamsui, Taiwan, R.O.C |
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Abstract: | Consider k (k 2) populations whose mean
i
and variance
i
2
are all unknown. For given control values 0 and
0
2
, we are interested in selecting some population whose mean is the largest in the qualified subset in which each mean is larger than or equal to 0 and whose variance is less than or equal to
0
2
. In this paper we focus on the normal populations in details. However, the analogous method can be applied for the cases other than normal in some situations. A Bayes approach is set up and an empirical Bayes procedure is proposed which has been shown to be asymptotically optimal with convergence rate of order O(ln2
n/n). A simulation study is carried out for the performance of the proposed procedure and it is found satisfactory. |
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Keywords: | Best population multiple criteria asymptotical optimality empirical Bayes rule convergence rate |
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