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Characterization of the asymptotic distribution of semiparametric M-estimators

Authors: Hidehiko Ichimura and Sokbae Lee
Date: 31 December 2010
Type: Journal Article, Journal of Econometrics, Vol. 159, No. 2, pp. 252--266
DOI: 10.1016/j.jeconom.2010.05.005

Abstract

This paper develops a concrete formula for the asymptotic distribution of two-step, possibly non-smooth semiparametric M-estimators under general misspecification. Our regularity conditions are relatively straightforward to verify and also weaker than those available in the literature. The first-stage nonparametric estimation may depend on finite dimensional parameters. We characterize: (1) conditions under which the first-stage estimation of nonparametric components do not affect the asymptotic distribution, (2) conditions under which the asymptotic distribution is affected by the derivatives of the first-stage nonparametric estimator with respect to the finite-dimensional parameters, and (3) conditions under which one can allow non-smooth objective functions. Our framework is illustrated by applying it to three examples: (1) profiled estimation of a single index quantile regression model, (2) semiparametric least squares estimation under model misspecification, and (3) a smoothed matching estimator.

Previous version:
Hidehiko Ichimura and Sokbae Lee August 2006, Characterization of the asymptotic distribution of semiparametric M-estimators, cemmap Working Paper, CWP15/06

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