A nonparametric empirical Bayes approach to adaptive minimax estimation

The general maximum likelihood empirical Bayes (GMLEB) method has been proven to possess optimal properties and demonstrated to have superior numerical performance in the Gaussian sequence model. Although it is known that nonparametric function estimation and the Gaussian sequence models are closely related, implementation of the GMLEB in function estimation problems still awaits careful analysis. In this paper, we consider adaptive estimation to inhomogeneous smoothness. We study the extent to which the optimality properties of the GMLEB can be carried out from the Gaussian sequence model to nonparametric function estimation. We demonstrate the proposed method’s superior performance in large sample size settings.