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A Simple Consistent Non-parametric Estimator of the Regression Function in a Truncated Sample

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  • Armando Levy

    (North Carolina State University)

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    Abstract

    Much recent work has focused on the estimation of regression functions in samples which are truncated or censored. Much of this work has focused on the estimation of a parametric regression function with an error distribution of unknown form. While these method relax a strong parametric assumption about which we seldom have a priori information, they still impose a strong parametric assumption on the regression equation (which is presumably the focus of the analysis). Here we take the other approach. An estimator is proposed for the problem of non-parametric regression when the sample is truncated above or below some known threshold of the dependent variable. We specify the error distribution up to a vector of parameters while estimating the regression function without assuming a parametric form. A simple ``backfit'' estimator based on an initial kernel smooth is proposed. We establish consistency results for this estimator when the error distribution is known up to a finite parameter vector and satisfies some regularity conditions. A small monte-carlo study is performed to ascertain the finite sample properties of the estimator. The estimator is found to perform well in our experiment: achieving reasonableaverage absolute errors relative to the maximum likelihood estimator- especially when truncation is severe.

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    Bibliographic Info

    Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0651.

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    Date of creation: 01 Aug 2000
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    Handle: RePEc:ecm:wc2000:0651

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    1. Lee, Lung-fei, 1994. "Semiparametric two-stage estimation of sample selection models subject to Tobit-type selection rules," Journal of Econometrics, Elsevier, vol. 61(2), pages 305-344, April.
    2. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
    3. Ruud, Paul A., 1986. "Consistent estimation of limited dependent variable models despite misspecification of distribution," Journal of Econometrics, Elsevier, vol. 32(1), pages 157-187, June.
    4. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
    5. 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.
    6. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-90, July.
    7. Goldberger, Arthur S., 1981. "Linear regression after selection," Journal of Econometrics, Elsevier, vol. 15(3), pages 357-366, April.
    8. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
    9. Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
    10. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    11. Duncan, Gregory M., 1986. "A semi-parametric censored regression estimator," Journal of Econometrics, Elsevier, vol. 32(1), pages 5-34, June.
    12. Newey, Whitney K., 1986. "Linear instrumental variable estimation of limited dependent variable models with endogenous explanatory variables," Journal of Econometrics, Elsevier, vol. 32(1), pages 127-141, June.
    13. Fernandez, Luis, 1986. "Non-parametric maximum likelihood estimation of censored regression models," Journal of Econometrics, Elsevier, vol. 32(1), pages 35-57, June.
    14. Powell, James L, 1986. "Symmetrically Trimmed Least Squares Estimation for Tobit Models," Econometrica, Econometric Society, vol. 54(6), pages 1435-60, November.
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