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Characterization of the asymptotic distribution of semiparametric M-estimators

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  • Hidehiko Ichimura

    ()
    (University of Tokyo - 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.

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Bibliographic Info

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

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Keywords: C13; C14; Semiparametric estimation; Two-step estimators;

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Citations

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Cited by:
  1. Rothe, Christoph & Firpo, Sergio, 2013. "Semiparametric Estimation and Inference Using Doubly Robust Moment Conditions," IZA Discussion Papers 7564, Institute for the Study of Labor (IZA).
  2. Le-Yu Chen & Sokbae 'Simon' Lee & Myung Jae Sung, 2013. "Maximum score estimation of preference parameters for a binary choice model under uncertainty," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP14/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. Pedro Carneiro & Sokbae 'Simon' Lee, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP01/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Horowitz, Joel L. & Lee, Sokbae, 2009. "Testing a parametric quantile-regression model with an endogenous explanatory variable against a nonparametric alternative," Journal of Econometrics, Elsevier, Elsevier, vol. 152(2), pages 141-152, October.
  5. Ying-Ying Lee, 2014. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Economics Series Working Papers 706, University of Oxford, Department of Economics.
  6. Koen Jochmans, 2013. "Pairwise-comparison estimation with nonparametric controls," Sciences Po Economics Discussion Papers 2013-04, Sciences Po Departement of Economics.
  7. Kasahara, Hiroyuki & Shimotsu, Katsumi, 2008. "Pseudo-likelihood estimation and bootstrap inference for structural discrete Markov decision models," Journal of Econometrics, Elsevier, Elsevier, vol. 146(1), pages 92-106, September.
  8. Tadao Hoshino, 2013. "Estimation of the preference heterogeneity within stated choice data using semiparametric varying-coefficient methods," Empirical Economics, Springer, Springer, vol. 45(3), pages 1129-1148, December.
  9. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2011. "Semiparametric Estimation with Generated Covariates," IZA Discussion Papers 6084, Institute for the Study of Labor (IZA).
  10. Hiroyuki Kasahara & Katsumi Shimotsu, 2006. "Nested Pseudo-likelihood Estimation and Bootstrap-based Inference for Structural Discrete Markov Decision Models," UWO Department of Economics Working Papers, University of Western Ontario, Department of Economics 20064, University of Western Ontario, Department of Economics.
  11. Juan Carlos Escanciano & David Jacho-Chavez & Arthur Lewbel, 2010. "Uniform Convergence of Weighted Sums of Non- and Semi-parametric Residuals for Estimation and Testing," Boston College Working Papers in Economics, Boston College Department of Economics 756, Boston College Department of Economics, revised 31 Jan 2012.
  12. Juan Carlos Escanciano & Lin Zhu, 2013. "Set inferences and sensitivity analysis in semiparametric conditionally identified models," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP55/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  13. Daniel Ackerberg & Xiaohong Chen & Jinyong Hahn, 2011. "Asymptotic Variance Estimator for Two-Step Semiparametric Estimators," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1803, Cowles Foundation for Research in Economics, Yale University.

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