Bandwidth Selection for Semiparametric Estimators Using the m-out-of-n Bootstrap∗

This paper considers a class of semiparametric estimators that take the form of density-weighted averages. These arise naturally in a consideration of semiparametric methods for the estimation of index and sample-selection models involving preliminary kernel density estimates. The question con-sidered in this paper is that of selecting the degree of smoothing to be used in computing the preliminary density estimate. This paper proposes a boot-strap method for estimating the mean squared error and associated optimal bandwidth. The particular bootstrap method suggested here involves using a resample of smaller size than the original sample. This method of band-width selection is presented with specific reference to the case of estimators of average densities, of density-weighted average derivatives and of density-weighted conditional covariances. JEL Classification: C1