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Characterization of the asymptotic distribution of semiparametric M-estimators

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  • Hidehiko Ichimura

    ()
    (Institute for Fiscal Studies and University of Tokyo)

  • Sokbae 'Simon' Lee

    ()
    (Institute for Fiscal Studies and 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 Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP15/06.

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Length: 39 pp.
Date of creation: Aug 2006
Date of revision:
Handle: RePEc:ifs:cemmap:15/06

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  1. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
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Citations

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Cited by:
  1. Koen Jochmans, 2013. "Pairwise‐comparison estimation with non‐parametric controls," Econometrics Journal, Royal Economic Society, vol. 16(3), pages 340-372, October.
  2. 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 20064, University of Western Ontario, Department of Economics.
  3. 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.
  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, vol. 152(2), pages 141-152, October.
  5. 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.
  6. 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.
  7. 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).
  8. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2011. "Semiparametric Estimation with Generated Covariates," IZA Discussion Papers 6084, Institute for the Study of Labor (IZA).
  9. 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.
  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. 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.
  12. 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.

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