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Semiparametric Estimation Of A Partially Linear Censored Regression Model

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  • Chen, Songnian
  • Khan, Shakeeb

Abstract

In this paper we propose an estimation procedure for a censored regression model where the latent regression function has a partially linear form. Based on a conditional quantile restriction, we estimate the model by a two stage procedure. The first stage nonparametrically estimates the conditional quantile function at in-sample and appropriate out-of-sample points, and the second stage involves a simple weighted least squares procedure. The proposed procedure is shown to have desirable asymptotic properties under regularity conditions that are standard in the literature. A small scale simulation study indicates that the estimator performs well in moderately sized samples.

Suggested Citation

  • Chen, Songnian & Khan, Shakeeb, 2001. "Semiparametric Estimation Of A Partially Linear Censored Regression Model," Econometric Theory, Cambridge University Press, vol. 17(3), pages 567-590, June.
    • Handle: RePEc:cup:etheor:v:17:y:2001:i:03:p:567-590_17
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    Cited by:

    1. Chernozhukov, Victor & Fernández-Val, Iván & Kowalski, Amanda E., 2015. "Quantile regression with censoring and endogeneity," Journal of Econometrics, Elsevier, vol. 186(1), pages 201-221.
    2. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    3. Choi, Jin-young & Lee, Myoung-jae, 2019. "Twins are more different than commonly believed, but made less different by compensating behaviors," Economics & Human Biology, Elsevier, vol. 35(C), pages 18-31.
    4. Xiaofeng Lv & Rui Li, 2013. "Smoothed empirical likelihood analysis of partially linear quantile regression models with missing response variables," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 317-347, October.
    5. Joseph G. Altonji & Hidehiko Ichimura & Taisuke Otsu, 2012. "Estimating Derivatives in Nonseparable Models With Limited Dependent Variables," Econometrica, Econometric Society, vol. 80(4), pages 1701-1719, July.
    6. De Silva, Dakshina G. & Kosmopoulou, Georgia & Lamarche, Carlos, 2017. "Subcontracting and the survival of plants in the road construction industry: A panel quantile regression analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 137(C), pages 113-131.
    7. Yiguo Sun, 2005. "Semiparametric Efficient Estimation of Partially Linear Quantile Regression Models," Annals of Economics and Finance, Society for AEF, vol. 6(1), pages 105-127, May.
    8. Xiaohong Chen & Oliver Linton & Ingred van Keilegom, 2002. "Estimation of semiparametric models when the criterion function is not smooth," CeMMAP working papers 02/02, Institute for Fiscal Studies.
    9. Peixin Zhao & Xinrong Tang, 2016. "Imputation based statistical inference for partially linear quantile regression models with missing responses," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 991-1009, November.
    10. Blundell, Richard & Powell, James L., 2007. "Censored regression quantiles with endogenous regressors," Journal of Econometrics, Elsevier, vol. 141(1), pages 65-83, November.
    11. Honore, Bo & Khan, Shakeeb & Powell, James L., 2002. "Quantile regression under random censoring," Journal of Econometrics, Elsevier, vol. 109(1), pages 67-105, July.
    12. Qu, Zhongjun & Yoon, Jungmo, 2015. "Nonparametric estimation and inference on conditional quantile processes," Journal of Econometrics, Elsevier, vol. 185(1), pages 1-19.
    13. Fabio Sigrist & Werner A. Stahel, 2010. "Using The Censored Gamma Distribution for Modeling Fractional Response Variables with an Application to Loss Given Default," Papers 1011.1796, arXiv.org, revised May 2012.
    14. Sun, Yiguo, 2006. "A Consistent Nonparametric Equality Test Of Conditional Quantile Functions," Econometric Theory, Cambridge University Press, vol. 22(4), pages 614-632, August.
    15. 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.
    16. Wu, Chaojiang & Yu, Yan, 2014. "Partially linear modeling of conditional quantiles using penalized splines," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 170-187.
    17. Sun, Y., 2003. "Square Root N - Consistent Semiparametric Estimation of Partially Linear Quantile Regression Models," Working Papers 2003-11, University of Guelph, Department of Economics and Finance.
    18. Moral-Arce, Ignacio & Rodríguez-Póo, Juan M. & Sperlich, Stefan, 2011. "Low dimensional semiparametric estimation in a censored regression model," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 118-129, January.
    19. Xiaoshuang Zhou & Peixin Zhao & Yujie Gai, 2022. "Imputation-based empirical likelihood inferences for partially nonlinear quantile regression models with missing responses," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 705-722, December.
    20. Guo, Jing & Wang, Lei & Zhang, Zhengyu, 2022. "Identification and estimation of a heteroskedastic censored regression model with random coefficient dummy endogenous regressors," Economic Modelling, Elsevier, vol. 110(C).

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