The Asymptotic Variance of Semiparametric Estimators.

This paper derives a general formula for the asymptotic variance of semiparametric estimators that accounts for the presence of nonparametric estimators of functions. The general formula is specialized to show invariance of the asymptotic variance to the type of nonparametric estimator and to obtain correction terms for estimation of densities and mean-square projections (including conditional expectations). Regularity conditions for the validity of the formula are also given, including primitive conditions for asymptotic normality when series estimators are present. New examples considered include a semiparametric panel probit estimator and a series estimator of the average derivative. Copyright 1994 by The Econometric Society.