A General Approach to Nonparametric Empirical Bayes Estimation

摘要

Let (X1,θ1), (X2, θ2), … ,(XN, θN), (XN+ 1, θN+ 1) be independent random vectors with each θidistributed according to some unknown prior densityg. Given θi, let Xihave the conditional density qi(xθi), i = 1, … ,N+ 1. In each pair the first component is observable, but the second is not. The objective is to estimate a known function b(θN+ 1) of θN+ 1