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Characterization of the Asymptotic Distribution of Semiparametric M-Estimators

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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.

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Bibliographic Info

Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-426.

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Length: 39pages
Date of creation: May 2006
Date of revision:
Handle: RePEc:tky:fseres:2006cf426

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References

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Citations

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Cited by:
  1. Juan Carlos Escanciano & Lin Zhu, 2013. "Set inferences and sensitivity analysis in semiparametric conditionally identified models," CeMMAP working papers CWP55/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Koen Jochmans, 2013. "Pairwise-comparison estimation with nonparametric controls," Sciences Po publications 2013-04, Sciences Po.
  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 CWP01/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. 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 CWP14/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. 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 756, Boston College Department of Economics, revised 31 Jan 2012.
  6. 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, vol. 152(2), pages 141-152, October.
  7. Rothe, Christoph & Firpo, Sergio, 2013. "Semiparametric estimation and inference using doubly robust moment conditions," Textos para discussão 330, Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
  8. Daniel Ackerberg & Xiaohong Chen & Jinyong Hahn, 2011. "Asymptotic Variance Estimator for Two-Step Semiparametric Estimators," Cowles Foundation Discussion Papers 1803, Cowles Foundation for Research in Economics, Yale University.
  9. Hiroyuki Kasahara & Katsumi Shimotsu, 2006. "Nested Pseudo-likelihood Estimation and Bootstrap-based Inference for Structural Discrete Markov Decision Models," Working Papers 1063, Queen's University, Department of Economics.
  10. 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.
  11. Enno Mammen & Christoph Rothe & Melanie Schienle, 2011. "Semiparametric Estimation with Generated Covariates," SFB 649 Discussion Papers SFB649DP2011-064, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  12. Kasahara, Hiroyuki & Shimotsu, Katsumi, 2008. "Pseudo-likelihood estimation and bootstrap inference for structural discrete Markov decision models," Journal of Econometrics, Elsevier, vol. 146(1), pages 92-106, September.

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