On monotonicity of regression quantile functions
AbstractIn the linear regression quantile model, the conditional quantile of the response, Y, given x is QYx([tau])[reverse not equivalent]x'[beta]([tau]). Though QYx([tau]) must be monotonically increasing, the Koenker-Bassett regression quantile estimator, , is not monotonic outside a vanishingly small neighborhood of . Given a grid of mesh [delta]n, let be the linear interpolation of the values of along the grid. We show here that for a range of rates, [delta]n, will be strictly monotonic (with probability tending to one) and will be asymptotically equivalent to in the sense that n1/2 times the difference tends to zero at a rate depending on [delta]n.
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 78 (2008)
Issue (Month): 10 (August)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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Journal of Economic Perspectives,
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