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Asymptotically Efficient Median Regression In The Presence Of Heteroskedasticity Of Unknown Form

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  • Zhao, Quanshui
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    Abstract

    We consider a linear model with heteroskedasticity of unknown form. Using Stone s (1977, Annals of Statistics 5, 595 645) k nearest neighbors (k-NN) estimation approach, the optimal weightings for efficient least absolute deviation regression are estimated consistently using residuals from preliminary estimation. The reweighted least absolute deviation or median regression estimator with the estimated weights is shown to be equivalent to the estimator using the true but unknown weights under mild conditions. Asymptotic normality of the estimators is also established. In the finite sample case, the proposed estimators are found to outperform the generalized least squares method of Robinson (1987, Econometrica 55, 875 891) and the one-step estimator of Newey and Powell (1990, Econometric Theory 6, 295 317) based on a Monte Carlo simulation experiment.

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    Bibliographic Info

    Article provided by Cambridge University Press in its journal Econometric Theory.

    Volume (Year): 17 (2001)
    Issue (Month): 04 (August)
    Pages: 765-784

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    Handle: RePEc:cup:etheor:v:17:y:2001:i:04:p:765-784_17

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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. Marilena Furno, 2012. "Tests for structural break in quantile regressions," AStA Advances in Statistical Analysis, Springer, vol. 96(4), pages 493-515, October.
    3. Ma, Lingjie & Koenker, Roger, 2006. "Quantile regression methods for recursive structural equation models," Journal of Econometrics, Elsevier, vol. 134(2), pages 471-506, October.
    4. Sweeney, Stuart & Davenport, Frank & Grace, Kathryn, 2013. "Combining insights from quantile and ordinal regression: Child malnutrition in Guatemala," Economics & Human Biology, Elsevier, vol. 11(2), pages 164-177.
    5. Lingjie Ma & Larry Pohlman, 2008. "Return forecasts and optimal portfolio construction: a quantile regression approach," The European Journal of Finance, Taylor & Francis Journals, vol. 14(5), pages 409-425.
    6. Otsu, Taisuke, 2008. "Conditional empirical likelihood estimation and inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 142(1), pages 508-538, January.
    7. He X. & Zhu L-X., 2003. "A Lack-of-Fit Test for Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1013-1022, January.
    8. Oberhofer, Walter & Haupt, Harry, 2003. "Nonlinear quantile regression under dependence and heterogeneity," University of Regensburg Working Papers in Business, Economics and Management Information Systems 388, University of Regensburg, Department of Economics.

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