On monotonicity of regression quantile functions

Neocleous, T. and Portnoy, S. (2008) On monotonicity of regression quantile functions. Statistics and Probability Letters, 78(10), pp. 1226-1229. (doi:10.1016/j.spl.2007.11.024)

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Publisher's URL: http://dx.doi.org/10.1016/j.spl.2007.11.024

Abstract

In the linear regression quantile model, the conditional quantile of the response, Y, given x is QY|x(τ)≡x′β(τ). Though QY|x(τ) must be monotonically increasing, the Koenker–Bassett regression quantile estimator, View the MathML source, is not monotonic outside a vanishingly small neighborhood of View the MathML source. Given a grid of mesh δn, let View the MathML source be the linear interpolation of the values of View the MathML source along the grid. We show here that for a range of rates, δn, View the MathML source will be strictly monotonic (with probability tending to one) and will be asymptotically equivalent to View the MathML source in the sense that n1/2 times the difference tends to zero at a rate depending on δn.

Item Type:Articles
Keywords:Regression quantile, monotonicity, Bahadur representation.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Neocleous, Dr Tereza
Authors: Neocleous, T., and Portnoy, S.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Statistics and Probability Letters
Publisher:Elsevier
ISSN:0167-7152
Copyright Holders:Copyright © 2008 Elsevier
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher.

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