A general approach to nonparametric empirical bayes estimation
Abbreviated Journal Title
empirical Bay estimation; posterior quadratic risk; convergence rate; reliability characteristics; RATES; MODELS; Statistics & Probability
Let (X(1), theta(1)), (X(2), theta(2)), ..., (X(N), theta(N)), (X(N+1), theta(N+1)) be independent random vectors with each theta(i) distributed according to some unknown prior density g. Given theta(i), let X(i) have the conditional density q(i)(x/theta(i)), 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(theta(N+1)) of theta(N+1). A general technique for construction of empirical Bayes estimators of b(theta(N+1)) is proposed and their convergence rates are examined. The special case, when the conditional densities q(i)(x/theta), i=1, ..., N+1, are identical, is also discussed. The theory is used to estimate of some reliability characteristics of nuclear power plant equipment.
"A general approach to nonparametric empirical bayes estimation" (1997). Faculty Bibliography 1990s. 2050.