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Nonparametric Censored Regression

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Abstract

The nonparametric censored regression model is y = max[c, m(x) + e], where both the regression function m(x) and the distribution of the error e are unknown, but the fixed censoring point c is known. This paper provides a simple consistent estimator of the derivative of m(x) with respect to each element of x. The convergence rate of this estimator is the same as for the derivatives of an uncensored nonparametric regression. We then estimate the regression function itself by solving the associated partial differential equation system. We show that our estimator of m(x) achieves the same rate of convergence as the usual estimators in uncensored nonparametric regression. We also provide root n estimates of weighted average derivatives of m(x), which equal the coefficients in any linear or partly linear specification for m(x).

Suggested Citation

  • Arthur Lewbel & Linton, Oliver Linton, 1998. "Nonparametric Censored Regression," Cowles Foundation Discussion Papers 1186, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1186
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    Cited by:

    1. Chen, Songnian & Khan, Shakeeb, 2000. "Estimating censored regression models in the presence of nonparametric multiplicative heteroskedasticity," Journal of Econometrics, Elsevier, vol. 98(2), pages 283-316, October.
    2. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 655-679.

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    More about this item

    Keywords

    Semiparametric; nonparametric; censored regression; Tobit; latent variable;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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