Monotone Empirical Bayes Tests for the Parameter of a Positive Exponential Family Using PA Samples

Abstract

In this paper, we develop an empirical Bayes (EB) test by using the kernel-type density estimation in the case of identically distributed and positively associated (PA) samples. Given some suitable conditions, the asymptotically optimal property and the convergence rate of the EB test are obtained. Furthermore, it is proven that the convergence rate can arbitrarily approach toO(n−1) . Finally, an example about the main results of this paper is given. This example shows that the rationality of the conditions in theorem.