Local polynomial fitting based on empirical likelihood

Abstract

A new nonparametric regression technique is proposed which involves the extension of local polynomial fitting to the empirical likelihood context, where the distribution of the stochastic error is not fully specified. The aim of this extension is to reduce the possible modelling bias of parametric likelihood and to allow one to use the auxiliary information about the stochastic error in the local polynomial fitting. The asymptotic bias and variance, consistency and asymptotic distribution of the proposed estimators are established. The proposed estimators are shown to inherit the main advantage of the local polynomial estimator based on the parametric likelihood over the Nadaraya-Watson kernel estimator near the boundaries. Moreover, the proposed estimators can be more flexible and efficient than the parametric likelihood based local polynomial estimator when the distribution of the stochastic error is misspecified. The new method is illustrated with applications to some simulated and real data sets.