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Nonparametric Censored and Truncated Regression

  • Arthur Lewbel


    (Boston College)

  • Oliver Linton


    (London School of Economics)

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. 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). An extension permits estimation in the presence of a general form of heteroskedasticity. We also extend the estimator to the nonparametric truncated regression model, in which only uncensored data points are observed.

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Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 439.

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Length: 29 pages
Date of creation: 05 Jan 2000
Date of revision:
Handle: RePEc:boc:bocoec:439
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  1. Ahn, Hyungtaik, 1995. "Nonparametric two-stage estimation of conditional choice probabilities in a binary choice model under uncertainty," Journal of Econometrics, Elsevier, vol. 67(2), pages 337-378, June.
  2. Andrews, Donald W K & Schafgans, Marcia M A, 1998. "Semiparametric Estimation of the Intercept of a Sample Selection Model," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 497-517, July.
  3. Fernandez, Luis, 1986. "Non-parametric maximum likelihood estimation of censored regression models," Journal of Econometrics, Elsevier, vol. 32(1), pages 35-57, June.
  4. Moshe Buchinsky & Jinyong Hahn, 1998. "An Alternative Estimator for the Censored Quantile Regression Model," Econometrica, Econometric Society, vol. 66(3), pages 653-672, May.
  5. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
  6. Duncan, Gregory M., 1986. "A semi-parametric censored regression estimator," Journal of Econometrics, Elsevier, vol. 32(1), pages 5-34, June.
  7. Dabrowska, D. M., 1995. "Nonparametric Regression with Censored Covariates," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 253-283, August.
  8. Wolfgang HÄRDLE & O. LINTON, 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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