Empirical Bayes test for scale exponential family

Abstract

In this paper, we consider the empirical Bayes (EB) test problem for the scale parameters in the scale exponential family with a weighted linear loss function. The EB test rules are constructed by the kernel estimation method. The asymptotical optimality and convergence rates of the EB test rules are obtained. The main results are illustrated by applying the proposed test to type II censored data from the exponential distribution and to the test problem for the dispersion parameter in the linear regression model.