Unbiasedness in Least Quantile Regression

Dirk Tasche

A chapter in Developments in Robust Statistics, 2003, pp 377-386 from Springer

Abstract: Summary We develop an abstract notion of regression which allows for a non-parametric formulation of unbiasedness. We prove then that least quantile regression is unbiased in this sense even in the heteroscedastic case if the error distribution has a continuous, symmetric, and uni-modal density. An example shows that unbiasedness may break down even for smooth and symmetric but not uni-modal error distributions. We compare these results to those for least MAD and least squares regression.

Keywords: Least quantile; Regression; Unbiasedness; Fisher consistency; Quantile derivative; Lord’s paradox (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-57338-5_33

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DOI: 10.1007/978-3-642-57338-5_33

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