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Nonparametric Censored and Truncated Regression

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  • Arthur Lewbel
  • Oliver Linton

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 estimators of m(x) and its derivatives. 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 linearr specifications for m(x). An extension permits estimation in the presence of a general form of heteroscedasticity. We also extend the estimator to the nonparametric truncated regression model, in which only uncensored data points are observed. The estimators are based on the relationship ?E(yk\x)/?m(x) = kE[yk-1/(y > 0)x ], which we show holds for positive integers k.

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Bibliographic Info

Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2000/389.

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Date of creation: Apr 2000
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Handle: RePEc:cep:stiecm:/2000/389

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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

Related research

Keywords: Semiparametric; nonparametric; censored regression; truncated regression; Tobit; latent variable;

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  1. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
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  12. Haerdle,Wolfgang & Stoker,Thomas, 1987. "Investigations smooth multiple regression by the method of average derivatives," Discussion Paper Serie A 107, University of Bonn, Germany.
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