Empirical Bayes testing for equivalence |
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Authors: | Lee-Shen Chen Ming-Chung Yang |
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Affiliation: | a Applied Statistics and Information Science, Ming Chuan University, Taoyuan, Taiwan b Graduate Institute of Statistics, National Central University, Chung-Li, Taiwan c Department of Banking and Finance, Kainan University, Taoyuan, Taiwan |
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Abstract: | For a fixed point θ0 and a positive value c0, this paper studies the problem of testing the hypotheses H0:|θ−θ0|≤c0 against H1:|θ−θ0|>c0 for the normal mean parameter θ using the empirical Bayes approach. With the accumulated past data, a monotone empirical Bayes test is constructed by mimicking the behavior of a monotone Bayes test. Such an empirical Bayes test is shown to be asymptotically optimal and its regret converges to zero at a rate (lnn)2.5/n where n is the number of past data available, when the current testing problem is considered. A simulation study is also given, and the results show that the proposed empirical Bayes procedure has good performance for small to moderately large sample sizes. Our proposed method can be applied for testing close to a control problem or testing the therapeutic equivalence of one standard treatment compared to another in clinical trials. |
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Keywords: | Asymptotically optimal Empirical Bayes test Equivalence Regret |
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