On monotonicity of regression quantile functions

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• 作者：Tereza Neocleous ; Stephen Portnoy
• 关键词：Thiomer ; Eudragit ; Chitosan microspheres ; Mucoadhesive ; Oral delivery ; Gamma imaging
• 刊名：Statistics and Probability Letters
• 出版年：2008
• 期刊代码：56_01677152
• 类别：mt
• 出版时间：1 August 2008
• 卷：78
• 期：10
• 页码：1226-1229
• 文件大小：204 K

摘要

In the linear regression quantile model, the conditional quantile of the response, Y, given x is Q_Y|x(τ)≡x^′β(τ). Though Q_Y|x(τ) must be monotonically increasing, the Koenker–Bassett regression quantile estimator, , is not monotonic outside a vanishingly small neighborhood of . Given a grid of mesh δ_n, let be the linear interpolation of the values of a200b347afacd5fa590a02ce73"> along the grid. We show here that for a range of rates, δ_n, will be strictly monotonic (with probability tending to one) and will be asymptotically equivalent to in the sense that n^1/2 times the difference tends to zero at a rate depending on δ_n.