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Characterization of the asymptotic distribution of semiparametric M-estimators

  • Hidehiko Ichimura

    ()

    (University of Tokyo - University of Tokyo)

  • Sokbae Lee

    ()

    (Department of Economics - University College London)

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.

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Paper provided by HAL in its series Post-Print with number peer-00741628.

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Date of creation: 15 Oct 2010
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Publication status: Published, Journal of Econometrics, 2010, 159, 2, 252
Handle: RePEc:hal:journl:peer-00741628
Note: View the original document on HAL open archive server: http://peer.ccsd.cnrs.fr/peer-00741628
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