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Characterization of the Asymptotic Distribution of Semiparametric M-Estimators

Author

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  • Hidehiko Ichimura

    (Faculty of Economics, University of Tokyo)

  • Sokbae Lee

    (Department of Economics, University College London)

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.

Suggested Citation

  • Hidehiko Ichimura & Sokbae Lee, 2006. "Characterization of the Asymptotic Distribution of Semiparametric M-Estimators," CIRJE F-Series CIRJE-F-426, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2006cf426
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    References listed on IDEAS

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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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