Characterization of the asymptotic distribution of semiparametric M-estimators

Hidehiko Ichimura and Sokbae (Simon) Lee

No CWP15/06, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

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.

Pages: 39 pp.
Date: 2006-08-06
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (13)

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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 (2010)
Working Paper: Characterization of the Asymptotic Distribution of Semiparametric M-Estimators (2006)
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