On monotonicity of regression quantile functions

Tereza Neocleous and Stephen Portnoy

Statistics & Probability Letters, 2008, vol. 78, issue 10, 1226-1229

Abstract: In 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.

Date: 2008
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