Bootstrapping local polynomial estimators in likelihood-based models

Abstract

The local likelihood estimator and a semiparametric bootstrap method are studied under weaker conditions than usual; it is not assumed that the true probability distribution underlying the observations is known and hence the local likelihood estimator might be based on an incorrect likelihood. Moreover, results are generalized to pseudolikelihood, which is based on a product of conditional densities. Strong consistency and asymptotic normality are derived under suitable regularity conditions and a study of the derivatives of the estimators is performed. It is shown that the bootstrap method leads to consistent estimators which can be used for constructing confidence regions. As an illustration, the local likelihood smoother and the bootstrap procedure are implemented for a selection of probability models for clustered binary data. A data example shows the method's applicability.