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Estimation of semiparametric models when the criterion function is not smooth

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  • Xiaohong Chen
  • Oliver Linton
  • Ingred van Keilegom

Abstract

We provide easy to verify suffcient 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 preliminary nonparametric estimators. Our results extend existing theories like those of Pakes and Pollard (1989),Andrews (1994a), and Newey (1994). We apply our results to two examples: a 'hit rate' and apartially linear median regression with some endogenous regressors.

Suggested Citation

  • Xiaohong Chen & Oliver Linton & Ingred van Keilegom, 2002. "Estimation of semiparametric models when the criterion function is not smooth," CeMMAP working papers 02/02, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:02/02
    DOI: 10.1920/wp.cem.2002.0202
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    References listed on IDEAS

    as
    1. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
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    3. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
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    6. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    7. 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.
    8. Chen, Songnian & Khan, Shakeeb, 2001. "Semiparametric Estimation Of A Partially Linear Censored Regression Model," Econometric Theory, Cambridge University Press, vol. 17(3), pages 567-590, June.
    9. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    10. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
    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.
    12. Michael G. Akritas & Ingrid Van Keilegom, 2001. "Non‐parametric Estimation of the Residual Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 549-567, September.
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