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Bandwidth Selection in Semiparametric Estimation of Censored Linear Regression Models

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  • Hall, Peter
  • Horowitz, Joel L.

Abstract

Quantile and semiparametric M estimation are methods for estimating a censored linear regression model without assuming that the distribution of the random component of the model belongs to a known parametric family. Both methods require estimating derivatives of the unknown cumulative distribution function of the random component. The derivatives can be estimated consistently using kernel estimators in the case of quantile estimation and finite difference quotients in the case of semiparametric M estimation. However, the resulting estimates of derivatives, as well as parameter estimates and inferences that depend on the derivatives, can be highly sensitive to the choice of the kernel and finite difference bandwidths. This paper discusses the theory of asymptotically optimal bandwidths for kernel and difference quotient estimation of the derivatives required for quantile and semiparametric M estimation, respectively. We do not present a fully automatic method for bandwidth selection.

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  • Hall, Peter & Horowitz, Joel L., 1990. "Bandwidth Selection in Semiparametric Estimation of Censored Linear Regression Models," Econometric Theory, Cambridge University Press, vol. 6(2), pages 123-150, June.
    • Handle: RePEc:cup:etheor:v:6:y:1990:i:02:p:123-150_00
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    Cited by:

    1. Joel L. Horowitz, 1998. "Bootstrap Methods for Median Regression Models," Econometrica, Econometric Society, vol. 66(6), pages 1327-1352, November.
    2. 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.
    3. Whang, Yoon-Jae, 2006. "Smoothed Empirical Likelihood Methods For Quantile Regression Models," Econometric Theory, Cambridge University Press, vol. 22(2), pages 173-205, April.
    4. Hochgürtel, S., 1997. "Precautionary Motives and Portfolio Decisions," Other publications TiSEM a6aa05be-cbd8-4f92-ac8e-8, Tilburg University, School of Economics and Management.
    5. Galvao, Antonio F. & Kato, Kengo, 2016. "Smoothed quantile regression for panel data," Journal of Econometrics, Elsevier, vol. 193(1), pages 92-112.
    6. Kengo Kato, 2012. "Asymptotic normality of Powell’s kernel estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 255-273, April.
    7. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    8. Hochgürtel, S., 1997. "Precautionary Motives and Portfolio Decisions," Discussion Paper 1997-55, Tilburg University, Center for Economic Research.
    9. Lewbel, Arthur & Schennach, Susanne M., 2007. "A simple ordered data estimator for inverse density weighted expectations," Journal of Econometrics, Elsevier, vol. 136(1), pages 189-211, January.

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