Empirical likelihood estimators for the error distribution in nonparametric regression models

Abstract

The aim of this paper is to show that existing estimators for the error distribution in nonparametric regression models can be improved when additional information about the distribution is included by the empirical likelihood method. The weak convergence of the resulting new estimator to a Gaussian process is shown and the performance is investigated by comparison of asymptotic mean squared errors and by means of a simulation study. As a by­product of our proofs we obtain stochastic expansions for smooth linear estimators based on residuals from the nonparametric regression model. AMS Classification: 62G08, 62G05