ASYMPTOTICS FOR SEMIPARAMETRIC ECONOMETRIC-MODELS VIA STOCHASTIC EQUICONTINUITY

This paper provides a general framework for proving the root T-consist ency and asymptotic normality of a wide variety of semiparametric esti mators. The class of estimators considered consists of estimators that can be defined as the solution to a minimization problem based on a c riterion function that may depend on a preliminary infinite dimensiona l nuisance parameter estimator. The method of proof exploits results c oncerning the stochastic equicontinuity of stochastic processes. The r esults are applied to the problem of semiparametric weighted least squ ares estimation of partially parametric regression models. Primitive c onditions are given for root T-consistency and asymptotic normality of this estimator.