IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/2060.html
   My bibliography  Save this paper

Nonparametric censored and truncated regression

Author

Listed:
  • Lewbel, Arthur
  • Linton, Oliver

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.

Suggested Citation

  • Lewbel, Arthur & Linton, Oliver, 2000. "Nonparametric censored and truncated regression," LSE Research Online Documents on Economics 2060, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:2060
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/2060/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    Other versions of this item:

    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.
    3. Duncan, Gregory M., 1986. "A semi-parametric censored regression estimator," Journal of Econometrics, Elsevier, vol. 32(1), pages 5-34, June.
    4. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
    5. Donald W. K. Andrews & Marcia M. A. Schafgans, 1998. "Semiparametric Estimation of the Intercept of a Sample Selection Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 497-517.
    6. Moshe Buchinsky & Jinyong Hahn, 1998. "An Alternative Estimator for the Censored Quantile Regression Model," Econometrica, Econometric Society, vol. 66(3), pages 653-672, May.
    7. 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.
    8. Dabrowska, D. M., 1995. "Nonparametric Regression with Censored Covariates," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 253-283, August.
    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.
    10. Fernandez, Luis, 1986. "Non-parametric maximum likelihood estimation of censored regression models," Journal of Econometrics, Elsevier, vol. 32(1), pages 35-57, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Arthur Lewbel & Linton, Oliver Linton, 1998. "Nonparametric Censored Regression," Cowles Foundation Discussion Papers 1186, Cowles Foundation for Research in Economics, Yale University.
    2. Honore, Bo & Khan, Shakeeb & Powell, James L., 2002. "Quantile regression under random censoring," Journal of Econometrics, Elsevier, vol. 109(1), pages 67-105, July.
    3. Honore, Bo E. & Kyriazidou, Ekaterini & Udry, Christopher, 1997. "Estimation of Type 3 Tobit models using symmetric trimming and pairwise comparisons," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 107-128.
    4. Melenberg, Bertrand & van Soest, Arthur, 1996. "Parametric and Semi-parametric Modelling of Vacation Expenditures," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(1), pages 59-76, Jan.-Feb..
    5. P. Čížek & S. Sadikoglu, 2018. "Bias-corrected quantile regression estimation of censored regression models," Statistical Papers, Springer, vol. 59(1), pages 215-247, March.
    6. Khan, Shakeeb & Powell, James L., 2001. "Two-step estimation of semiparametric censored regression models," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 73-110, July.
    7. Armando Levy, 2000. "A Simple Consistent Non-parametric Estimator of the Regression Function in a Truncated Sample," Econometric Society World Congress 2000 Contributed Papers 0651, Econometric Society.
    8. Randall A. Lewis & James B. McDonald, 2014. "Partially Adaptive Estimation of the Censored Regression Model," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 732-750, October.
    9. Stephen R. Cosslett, 2003. "Efficient Semiparametric Estimation of Censored and Truncated Regressions via a Smoothed Self-Consistency Equation," Working Papers 03-05, Ohio State University, Department of Economics.
    10. Chen, Songnian, 1997. "Semiparametric estimation of the Type-3 Tobit model," Journal of Econometrics, Elsevier, vol. 80(1), pages 1-34, September.
    11. Tsur, Yacov & Zemel, Amos, 1990. "Iterative Least Squares Estimation Of Censored Regression Models With Unknown Error Distributions," Staff Papers 14118, University of Minnesota, Department of Applied Economics.
    12. Maria Karlsson & Thomas Laitila, 2014. "Finite mixture modeling of censored regression models," Statistical Papers, Springer, vol. 55(3), pages 627-642, August.
    13. Lu, Xuewen & Burke, M.D., 2005. "Censored multiple regression by the method of average derivatives," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 182-205, July.
    14. 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.
    15. Lu, Xuewen & Cheng, Tsung-Lin, 2007. "Randomly censored partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1895-1922, November.
    16. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    17. McDonald, James B. & Xu, Yexiao J., 1996. "A comparison of semi-parametric and partially adaptive estimators of the censored regression model with possibly skewed and leptokurtic error distributions," Economics Letters, Elsevier, vol. 51(2), pages 153-159, May.
    18. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    19. Wilke, Ralf A. & Wichert, Laura, 2005. "Application of a simple nonparametric conditional quantile function estimator in unemployment duration analysis," ZEW Discussion Papers 05-67 [rev.], ZEW - Leibniz Centre for European Economic Research.
    20. Fernández, Ana I. & Rodríguez-Póo, Juan M. & Sperlich, Stefan, 1998. "Semiparametric three step estimation methods in labor supply models," SFB 373 Discussion Papers 1998,71, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.

    More about this item

    Keywords

    Semiparametric; nonparametric; censored regression; truncated 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
    • 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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ehl:lserod:2060. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.