Two-Sided Empirical Bayes Test for the Exponential Family with Contaminated Data
CHEN Jiaqing1, JIN Qianyu1, CHEN Zhiqiang1, LIU Cihua2 1. College of Science, Wuhan University of Technology, Wuhan 430070, Hubei, China; 2. College of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China
In this study, the two-sided Empirical Bayes test (EBT) rules for the parameter of continuous one-parameter exponential family with contaminated data (errors in variables) are constructed by a deconvolution kernel method. The asymptotically optimal uniformly over a class of prior distributions and uniform rates of convergence, which depends on two types of the error distributions for the proposed EBT rules, are obtained under suitable con- ditions. Finally, an example about the main results of this paper is given.
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