A Nonparametric Regression Estimator that Adapts to Error Distribution of Unknown Form

Abstract

We propose a new estimator for nonparametric regression based on local likelihood estimation using an estimated error score function obtained from the residuals of a preliminary nonparametric regression. We show that our estimator is asymptotically equivalent to the infeasible local maximum likelihood estimator [Staniswalis (1989)], and hence improves on standard kernel estimators when the error distribution is not normal. We investigate the finite sample performance of our procedure on simulated data.