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Nonparametric Censored and Truncated Regression

Author

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  • Arthur Lewbel

    (Boston College)

  • Oliver Linton

    (Yale University and London School of Economics)

Abstract

The nonparametric censored regression model, with a fixed, known censoring point (normalized to zero), is y=max[0,m(x)+e], where both the regression function m(x) and the distribution of the error e are unknown. This paper provides consistent estimators of m(x) and its derivatives with respect to each element of x. The convergence rate is the same as for an uncensored nonparametric regression and its derivatives. We also provide root n estimates of weighted average derivatives of m(x), which equal the coefficients in linear or partly linear specifications for m(x). Some estimators already exist for randomly censored nonparametric models, but we provide estimators for fixed censoring, and for truncated regression. The estimators are based on the relationship that the derivative of E(y|x) with respect to m(x) equals E[I(y>0)|x]. We derive A similar expression involving higher moments of y also, which is required for the truncated regression model. An advantage of our estimator is that, unlike quantile methods, no a priori information is required regarding the degree of censoring at each x. Also error symmetry is not assumed. Another advantage is that our estimator extends to nonparametric truncated regression, so m(x) and its derivates can be estimated when only observations having m(x) + e > 0 are observed. We also provide an extension that permits estimation in the presence of a general form of heteroscedasticity.

Suggested Citation

  • Arthur Lewbel & Oliver Linton, 2000. "Nonparametric Censored and Truncated Regression," Econometric Society World Congress 2000 Contributed Papers 1237, Econometric Society.
  • Handle: RePEc:ecm:wc2000:1237
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    References listed on IDEAS

    as
    1. Horowitz, Joel L., 1986. "A distribution-free least squares estimator for censored linear regression models," Journal of Econometrics, Elsevier, vol. 32(1), pages 59-84, June.
    2. Härdle, Wolfgang & Linton, O., 1995. "Nonparametric Regression," SFB 373 Discussion Papers 1995,29, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    5. Donald W. K. Andrews & Marcia M. A. Schafgans, 1998. "Semiparametric Estimation of the Intercept of a Sample Selection Model," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 497-517.
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    More about this item

    JEL classification:

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

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