Characterization of the asymptotic distribution of semiparametric M-estimators

Hidehiko Ichimura and Sokbae (Simon) Lee

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.

Keywords: C13; C14; Semiparametric estimation; Two-step estimators (search for similar items in EconPapers)
Date: 2010-10-15
Note: View the original document on HAL open archive server: https://hal.science/hal-00741628
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Citations: View citations in EconPapers (48)

Published in Econometrics, 2010, 159 (2), pp.252. ⟨10.1016/j.jeconom.2010.05.005⟩

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Related works:
Journal Article: Characterization of the asymptotic distribution of semiparametric M-estimators (2010)
Working Paper: Characterization of the asymptotic distribution of semiparametric M-estimators (2006)
Working Paper: Characterization of the Asymptotic Distribution of Semiparametric M-Estimators (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00741628

DOI: 10.1016/j.jeconom.2010.05.005

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