Advanced Applications in Acoustics, Noise and Vibration, Frank Fahy, John Walker (Eds.). Published by Spon Press/Taylor & Francis Group, London, UK (2004), pp. 1–640, £120.00, ISBN: 0
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In the linear regression quantile model, the conditional quantile of the response, Y, given x is QY|x(τ)≡xβ(τ). Though QY|x(τ) must be monotonically increasing, the Koenker–Bassett regression quantile estimator, 90be3302c4246964de7ca567b21f7b9c"">, is not monotonic outside a vanishingly small neighborhood of b36c0ffc"">. Given a grid of mesh δn, let be the linear interpolation of the values of 0b347afacd5fa590a02ce73""> along the grid. We show here that for a range of rates, δn, 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 δn.

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