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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

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    7. 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.
    8. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    9. 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.
    10. 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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