U-Processes in the Analysis of a Generalized Semiparametric Regression Estimator

Abstract

We prove -consistency and asymptotic normality of a generalized semiparametric regression estimator that includes as special cases Ichimura's semiparametric least-squares estimator for single index models, and the estimator of Klein and Spady for the binary choice regression model. Two function expansions reveal a type of U-process structure in the criterion function; then new U-process maximal inequalities are applied to establish the requisite stochastic equicontinuity condition. This method of proof avoids much of the technical detail required by more traditional methods of analysis. The general framework suggests other -consistent and asymptotically normal estimators.