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Estimation of Semiparametric Models when the Criterion Function Is Not Smooth

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  • Xiaohong Chen
  • Oliver Linton
  • Ingrid Van Keilegom

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 such as 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. Copyright The Econometric Society 2003.

Suggested Citation

  • Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
  • Handle: RePEc:ecm:emetrp:v:71:y:2003:i:5:p:1591-1608
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    References listed on IDEAS

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    1. Joel L. Horowitz, 1998. "Bootstrap Methods for Median Regression Models," Econometrica, Econometric Society, vol. 66(6), pages 1327-1352, November.
    2. Arthur Lewbel & Oliver Linton, 2002. "Nonparametric Censored and Truncated Regression," Econometrica, Econometric Society, vol. 70(2), pages 765-779, March.
    3. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    4. Donald J. Brown & Marten H. Wegkamp, 2002. "Weighted Minimum Mean-Square Distance from Independence Estimation," Econometrica, Econometric Society, vol. 70(5), pages 2035-2051, September.
    5. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    6. Richard W. Blundell & Martin Browning & Ian A. Crawford, 2003. "Nonparametric Engel Curves and Revealed Preference," Econometrica, Econometric Society, vol. 71(1), pages 205-240, January.
    7. Linton, O. B. & Chen, R. & Härdle, Wolfgang, 1995. "An Analysis of Transformations for Additive Nonparanetric Regression," SFB 373 Discussion Papers 1995,68, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    8. 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.
    9. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    10. Manski, Charles F, 1983. "Closest Empirical Distribution Estimation," Econometrica, Econometric Society, vol. 51(2), pages 305-319, March.
    11. 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.
    12. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
    13. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    14. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
    15. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    16. 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, June.
    17. repec:cup:etheor:v:11:y:1995:i:3:p:560-96 is not listed on IDEAS
    18. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    19. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
    20. 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.
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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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