Empirical Bayes Decision for a Generalized Exponential Distribution with Contaminated Data

Abstract

The two-sided and one-sided empirical Bayes test (EBT) rules for the parameter of a generalized exponential distribution with contaminated data (errors in variables) are constructed by a deconvolution kernel method, respectively. Under the type of the supersmooth error distributions and the supersmooth errors with the error level can be controlled situations, the asymptotically optimal uniformly over a class of prior distributions and uniform rates of convergence of the corresponding regret for the proposed EBT rules are obtained with suitable conditions. The example study shows that the assumptions and conditions of the main results of this paper are satisfied easily by calculating.