Asymptotically Efficient Median Regression In The Presence Of Heteroskedasticity Of Unknown Form
AbstractWe 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 InfoArticle provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 17 (2001)
Issue (Month): 04 (August)
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