On empirical Bayes estimation in the location family

This paper considers empirical Bayes (EB) squared error loss estimation (SELE) in the location family. That is, the component problem is the SELE of theta based on an observation Y having conditional (on theta) density of the form f(0)(y - theta) for some known density function f(0). An EB estimator is constructed based on kernel type estimator of the unknown prior density using deconvolution techniques. It is shown that the proposed EB estimator is asymptotically optimal. Uniform rates of convergence of the regret are also exhibited. This paper presents a generalization to the existing results on the same problem considered for the normal (theta, 1) uniform (theta, theta + 1) and translated exponential (theta) distributions.