Convergence Rate of Empirical Bayes for Two-Parameter Exponential Distribution with Replicated Data

Abstract

In this paper, empirical Bayes test for a parameter $θ$ of two-parameter exponential distribution is investigated with replicated past data. Under some conditions, the asymptotically optimal property is obtained. It is indicated that the rate of convergence can be very close to $O(N^{−\frac{1}{2}})$ in this case that a parameter $µ$ is known.