Monotone Empirical Bayes Tests Based on Kernel Sequence Estimation

摘要

Empirical Bayes inference problems involve the estimation of unknown functions (a density and its derivative). It is well known that this can be done through the kernel method, i.e. using a fixed index kernel and varied window bandwidth. In this paper, we introduce the kernel sequence method which considers using a sequence of kernel functions and allows the kernel index and window bandwidth to vary simultaneously in the estimates. This method usually produces better estimates since varied kernels give us more flexibility to do so. We apply the above method to the construction of the monotone empirical Bayes test for the general continuous one-parameter exponential family.