Bootstrap-based Bandwidth Selection for Semiparametric Generalized Regression Estimators

Abstract

This paper considers the problem of implementing semiparametric extremum estimators of a generalized regression model with an unknown link function. The class of estimator under consideration includes as special cases the semiparametric least-squares estimator of Ichimura (1993) as well as the semiparametric quasi-likelihood estimator of Klein and Spady (1993). In general, it is assumed to involve the computation of a nonparametric kernel estimate of the link function that appears in place of the true, but unknown, link function in the appropriate location in a smooth criterion function. The specific question considered in this paper concerns the practical selection of the degree of smoothing to be used in computing the nonparametric regression estimate. This paper proposes a method for selecting the smoothing parameter via resampling. The particular method suggested here involves using a resample of smaller size than the original sample. Specific guidance on selecting the resample size is given, and simulation evidence is presented to illustrate the utility of this method for samples of moderate size.Bandwidth selection, semiparametric, single-index model, bootstrap, m-out-of-n bootstrap, kernel smoothing