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Efficient Semiparametric Estimation of Censored and Truncated Regressions via a Smoothed Self-Consistency Equation

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  • Stephen R. Cosslett

Abstract

An asymptotically efficient likelihood-based semiparametric estimator is derived for the censored regression (tobit) model, based on a new approach for estimating the density function of the residuals in a partially observed regression. Smoothing the self-consistency equation for the nonparametric maximum likelihood estimator of the distribution of the residuals yields an integral equation, which in some cases can be solved explicitly. The resulting estimated density is smooth enough to be used in a practical implementation of the profile likelihood estimator, but is sufficiently close to the nonparametric maximum likelihood estimator to allow estimation of the semiparametric efficient score. The parameter estimates obtained by solving the estimated score equations are then asymptotically efficient. A summary of analogous results for truncated regression is also given. Copyright The Econometric Society 2004.

Suggested Citation

  • Stephen R. Cosslett, 2004. "Efficient Semiparametric Estimation of Censored and Truncated Regressions via a Smoothed Self-Consistency Equation," Econometrica, Econometric Society, vol. 72(4), pages 1277-1293, July.
    • Handle: RePEc:ecm:emetrp:v:72:y:2004:i:4:p:1277-1293
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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2004.00532.x
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    Cited by:

    1. James B. McDonald & Hieu Nguyen, 2012. "Heteroskedasticity and Distributional Assumptions in the Censored Regression Model," BYU Macroeconomics and Computational Laboratory Working Paper Series 2012-09, Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory.
    2. Cosslett, Stephen R., 2013. "Efficient semiparametric estimation for endogenously stratified regression via smoothed likelihood," Journal of Econometrics, Elsevier, vol. 177(1), pages 116-129.
    3. Kanaya, Shin, 2017. "Uniform Convergence Rates Of Kernel-Based Nonparametric Estimators For Continuous Time Diffusion Processes: A Damping Function Approach," Econometric Theory, Cambridge University Press, vol. 33(4), pages 874-914, August.
    4. Chen, Songnian & Zhou, Xianbo, 2012. "Semiparametric estimation of a truncated regression model," Journal of Econometrics, Elsevier, vol. 167(2), pages 297-304.
    5. Khan, Shakeeb & Tamer, Elie, 2009. "Inference on endogenously censored regression models using conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 152(2), pages 104-119, October.
    6. Keiding, Niels & Fine, Jason P. & Hansen, Oluf H. & Slama, Rémy, 2011. "Accelerated failure time regression for backward recurrence times and current durations," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 724-729, July.
    7. Lin, Guixian & He, Xuming & Portnoy, Stephen, 2012. "Quantile regression with doubly censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 797-812.
    8. Zhou, Xianbo & Pan, Zhewen, 2015. "Two-step semiparametric estimation of the Type-3 Tobit model," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 96-105.
    9. Jerry Hausman & Haoyang Liu & Ye Luo & Christopher Palmer, 2021. "Errors in the Dependent Variable of Quantile Regression Models," Econometrica, Econometric Society, vol. 89(2), pages 849-873, March.
    10. Jason Cook & James McDonald, 2013. "Partially Adaptive Estimation of Interval Censored Regression Models," Computational Economics, Springer;Society for Computational Economics, vol. 42(1), pages 119-131, June.
    11. Brantly Callaway & Tong Li & Irina Murtazashvili, 2021. "Nonlinear Approaches to Intergenerational Income Mobility allowing for Measurement Error," Papers 2107.09235, arXiv.org, revised Dec 2021.
    12. Komunjer, Ivana & Vuong, Quang, 2010. "Efficient estimation in dynamic conditional quantile models," Journal of Econometrics, Elsevier, vol. 157(2), pages 272-285, August.
    13. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    14. Ao Yuan, 2009. "Semiparametric inference with kernel likelihood," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(2), pages 207-228.

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