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Estimation of Semiparametric Models when the Criterion Function is not Smooth

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Author Info
Xiaohong Chen
Oliver Linton
Ingrid Van Keilegom

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Abstract

We provide easy to verify sufficient conditions for the consistency and asymptotic normality of a class of semiparametric optimization estimators where the criterion function does not obey standard smoothness conditions and simultaneously depends on some nonparametric estimators that can themselves depend on the parameters to be estimated. Our results extend existing theories like those of Pakes and Pollard (1989), Andrews (1994a) and Newey (1994). We also show that bootstrap provides asymptotically correct confidence regions for the finite dimensional parameters. We apply our results to two examples: a 'hit rate' and a partially linear median regression with some endogenous regressors.

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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2003/450.

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Date of creation: May 2003
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Handle: RePEc:cep:stiecm:/2003/450

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Related research
Keywords: Empirical processes non-smooth criterion semiparametric estimation stochastic equicontinuity.

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Richard Blundell & Martin Browning & Ian Crawford, 2002. "Nonparametric Engel Curves and Revealed Preference," CAM Working Papers 2002-04, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics. [Downloadable!]
    Other versions:
  2. Manski, Charles F, 1983. "Closest Empirical Distribution Estimation," Econometrica, Econometric Society, vol. 51(2), pages 305-19, March. [Downloadable!] (restricted)
  3. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
  4. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-82, November. [Downloadable!] (restricted)
  5. Joel L. Horowitz, 1998. "Bootstrap Methods for Median Regression Models," Econometrica, Econometric Society, vol. 66(6), pages 1327-1352, November.
    Other versions:
  6. Lee, Sokbae, 2003. "Efficient Semiparametric Estimation Of A Partially Linear Quantile Regression Model," Econometric Theory, Cambridge University Press, vol. 19(01), pages 1-31, January. [Downloadable!]
  7. Chen, Songnian & Khan, Shakeeb, 2001. "Semiparametric Estimation Of A Partially Linear Censored Regression Model," Econometric Theory, Cambridge University Press, vol. 17(03), pages 567-590, July. [Downloadable!]
  8. Arthur Lewbel & Oliver Linton, 2002. "Nonparametric Censored and Truncated Regression," Econometrica, Econometric Society, vol. 70(2), pages 765-779, March. [Downloadable!] (restricted)
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  9. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January. [Downloadable!] (restricted)
  10. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July. [Downloadable!] (restricted)
  11. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August. [Downloadable!] (restricted)
  12. Pakes, Ariel & Olley, Steven, 1995. "A limit theorem for a smooth class of semiparametric estimators," Journal of Econometrics, Elsevier, vol. 65(1), pages 295-332, January. [Downloadable!] (restricted)
  13. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July. [Downloadable!] (restricted)
  14. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May. [Downloadable!] (restricted)
  15. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September. [Downloadable!] (restricted)
  16. W. H"Ardle & O. Linton, . "Nonparametric Regression," Sonderforschungsbereich 373 1995-29, Humboldt Universitaet Berlin.
  17. repec:cup:etheor:v:11:y:1995:i:3:p:560-96 is not listed on IDEAS
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  1. Joel Horowitz & Sokbae 'Simon' Lee, 2007. "Testing a parametric quantile-regression model with an endogenous explanatory variable against a nonparametric alternative," CeMMAP working papers CWP02/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  2. Vincenzo Atella & Noemi Pace & Daniela Vuri, 2008. "Are employers discriminating with respect to weight? European Evidence using Quantile Regression," CEIS Research Paper 123, Tor Vergata University, CEIS, revised 14 Jul 2008. [Downloadable!]
  3. Christelle Viauroux, G.L. Gayle, 2004. "Root-N Consistent Semiparametric Eestimators of a Dynamic Panel Sample Selection Model," University of Cincinnati, Economics Working Papers Series 2004-05, University of Cincinnati, Department of Economics. [Downloadable!]
    Other versions:
  4. Hidehiko Ichimura, 2006. "Characterization of the Asymptotic Distribution of Semiparametric M-Estimators," CIRJE F-Series CIRJE-F-426, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
    Other versions:
  5. Sokbae Lee, 2004. "Endogeneity in Quantile Regression Models: A Control Function Approach," Econometric Society 2004 North American Summer Meetings 521, Econometric Society. [Downloadable!]
    Other versions:
  6. Cristian Huse, 2004. "Comparing Nonparametric Regression Quantiles," Econometric Society 2004 Latin American Meetings 165, Econometric Society. [Downloadable!]
  7. Yingyao Hu & Arthur Lewbel, 2008. "Identifying the returns to lying when the truth is unobserved," CeMMAP working papers CWP06/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
    Other versions:
  8. Oliver Linton1 & Kyungchul Song & Yoon-Jae Whang, 2008. "Bootstrap Tests of Stochastic Dominance with Asymptotic Similarity on the Boundary," PIER Working Paper Archive 08-006, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [Downloadable!]
  9. Kyungchul Song, 2007. "Testing Conditional Independence via Rosenblatt Transforms," PIER Working Paper Archive 07-026, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [Downloadable!]
  10. Yanqin Fan & Xiaohong Chen, 2004. "Estimation of Copula-Based Semiparametric Time Series Models," Econometric Society 2004 Far Eastern Meetings 559, Econometric Society. [Downloadable!]
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