Bootstrapping local polynomial estimators in likelihoodbased models

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 un-derlying 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 esti-mators is performed. It is shown that the bootstrap method leads to consistent estimators which can be used for constructing con¯dence 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