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Nonparametric Censored and Truncated Regression

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Author Info
Arthur Lewbel () (Boston College)
Oliver Linton () (London School of Economics)

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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. 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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Publisher Info
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
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Handle: RePEc:boc:bocoec:439

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Duncan, Gregory M., 1986. "A semi-parametric censored regression estimator," Journal of Econometrics, Elsevier, vol. 32(1), pages 5-34, June. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. Lewbel, Arthur, 1997. "Semiparametric Estimation of Location and Other Discrete Choice Moments," Econometric Theory, Cambridge University Press, vol. 13(01), pages 32-51, February. [Downloadable!]
  4. Moon, Choon-Geol, 1989. "A Monte Carlo Comparison of Semiparametric Tobit Estimators," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(4), pages 361-82, Oct.-Dec.. [Downloadable!] (restricted)
  5. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-82, November. [Downloadable!] (restricted)
  6. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November. [Downloadable!] (restricted)
  7. repec:cup:etheor:v:13:y:1997:i:1:p:32-51 is not listed on IDEAS
  8. Horowitz, J.L., 1998. "Nonparametric Estimation of a Generalized Additive Model with an Unknown Link Function," Working Papers 98-05, University of Iowa, Department of Economics.
  9. Honore, Bo E. & Powell, James L., 1994. "Pairwise difference estimators of censored and truncated regression models," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 241-278. [Downloadable!] (restricted)
  10. Wolfgang Hardle & Oliver Linton, 1994. "Applied Nonparametric Methods," Cowles Foundation Discussion Papers 1069, Cowles Foundation, Yale University. [Downloadable!]
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  11. Hausman, Jerry A & Newey, Whitney K, 1995. "Nonparametric Estimation of Exact Consumers Surplus and Deadweight Loss," Econometrica, Econometric Society, vol. 63(6), pages 1445-76, November. [Downloadable!] (restricted)
  12. Fernandez, Luis, 1986. "Non-parametric maximum likelihood estimation of censored regression models," Journal of Econometrics, Elsevier, vol. 32(1), pages 35-57, June. [Downloadable!] (restricted)
  13. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
  14. Andrews, Donald W K & Schafgans, Marcia M A, 1998. "Semiparametric Estimation of the Intercept of a Sample Selection Model," Review of Economic Studies, Blackwell Publishing, vol. 65(3), pages 497-517, July. [Downloadable!] (restricted)
  15. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July. [Downloadable!] (restricted)
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  16. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June. [Downloadable!]
  17. Dabrowska, D. M., 1995. "Nonparametric Regression with Censored Covariates," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 253-283, August. [Downloadable!] (restricted)
  18. McDonald, John F & Moffitt, Robert A, 1980. "The Uses of Tobit Analysis," The Review of Economics and Statistics, MIT Press, vol. 62(2), pages 318-21, May. [Downloadable!] (restricted)
  19. J. Horowitz, . "Nonparametric Estimation of a Generalized Additive Model with an Unknown Link Function," Sonderforschungsbereich 373 1998-83, Humboldt Universitaet Berlin.
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  20. repec:cup:etheor:v:11:y:1995:i:3:p:560-96 is not listed on IDEAS
  21. Moshe Buchinsky & Jinyong Hahn, 1998. "An Alternative Estimator for the Censored Quantile Regression Model," Econometrica, Econometric Society, vol. 66(3), pages 653-672, May.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function is not Smooth," STICERD - Econometrics Paper Series /2003/450, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
    Other versions:
  2. Joseph G. Altonji & Hidehiko Ichimura & Taisuke Otsu, 2008. "Estimating Derivatives in Nonseparable Models with Limited Dependent Variables," NBER Working Papers 14161, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  3. Byeong U. Park & Leopold Simar & Valentin Zelenyuk, 2008. "Local Likelihood Estimation of Truncated Regression and Its Partial Derivatives: Theory and Application," Discussion Papers 7, Kyiv School of Economics. [Downloadable!]
    Other versions:
  4. Elias Ould-Saïd & Mohamed Lemdani, 2006. "Asymptotic Properties of a Nonparametric Regression Function Estimator with Randomly Truncated Data," Annals of the Institute of Statistical Mathematics, Springer, vol. 58(2), pages 357-378, June. [Downloadable!] (restricted)
  5. Anil Kumar, 2005. "Nonparametric estimation of the impact of taxes on female labor supply," Working Papers 05-05, Federal Reserve Bank of Dallas. [Downloadable!]
  6. Cizek, P., 2008. "Semiparametric Robust Estimation of Truncated and Censored Regression Models," Discussion Paper 2008-34, Tilburg University, Center for Economic Research. [Downloadable!]
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