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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
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    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.

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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2004.00532.x
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    Bibliographic Info

    Article provided by Econometric Society in its journal Econometrica.

    Volume (Year): 72 (2004)
    Issue (Month): 4 (07)
    Pages: 1277-1293

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    Handle: RePEc:ecm:emetrp:v:72:y:2004:i:4:p:1277-1293

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    Cited by:
    1. Komunjer, Ivana & Vuong, Quang, 2010. "Efficient estimation in dynamic conditional quantile models," Journal of Econometrics, Elsevier, vol. 157(2), pages 272-285, August.
    2. Lin, Guixian & He, Xuming & Portnoy, Stephen, 2012. "Quantile regression with doubly censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 797-812.
    3. 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.
    4. Jason Cook & James McDonald, 2013. "Partially Adaptive Estimation of Interval Censored Regression Models," Computational Economics, Society for Computational Economics, vol. 42(1), pages 119-131, June.
    5. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    6. 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.
    7. 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.
    8. Chen, Songnian & Zhou, Xianbo, 2012. "Semiparametric estimation of a truncated regression model," Journal of Econometrics, Elsevier, vol. 167(2), pages 297-304.
    9. Cosslett, Stephen R., 2013. "Efficient semiparametric estimation for endogenously stratified regression via smoothed likelihood," Journal of Econometrics, Elsevier, vol. 177(1), pages 116-129.

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