Empirical Smoothing Parameter Selection in Adaptive Estimation

Abstract

We provide a solution to the smoothing parameter selection problem involved in the construction of adaptive estimates for the symmetric location model and the general linear model. Linear $B$-splines are used to give a simple form of the estimate of the score function of the underlying density. New empirical methods are proposed to locate the knots optimally and to select the number of knots. We also give asymptotic bounds for the empirical selection method and show that an estimate with an empirically selected smoothing parameter is adaptive. Our estimates are easy to compute and possess useful computational features. Simulation studies reveal that our estimates perform well in comparison with some well-known estimates.