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Non-crossing non-parametric estimates of quantile curves

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  • Holger Dette
  • Stanislav Volgushev
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    Abstract

    Since the introduction by Koenker and Bassett, quantile regression has become increasingly important in many applications. However, many non-parametric conditional quantile estimates yield crossing quantile curves (calculated for various "p"  is an element of  (0, 1)). We propose a new non-parametric estimate of conditional quantiles that avoids this problem. The method uses an initial estimate of the conditional distribution function in the first step and solves the problem of inversion and monotonization with respect to "p"  is an element of  (0, 1) simultaneously. It is demonstrated that the new estimates are asymptotically normally distributed with the same asymptotic bias and variance as quantile estimates that are obtained by inversion of a locally constant or locally linear smoothed conditional distribution function. The performance of the new procedure is illustrated by means of a simulation study and some comparisons with the currently available procedures which are similar in spirit with the method proposed are presented. Copyright (c) 2008 Royal Statistical Society.

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    Bibliographic Info

    Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).

    Volume (Year): 70 (2008)
    Issue (Month): 3 ()
    Pages: 609-627

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    Handle: RePEc:bla:jorssb:v:70:y:2008:i:3:p:609-627

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    Cited by:
    1. Roger Koenker & Samantha Leorato & Franco Peracchi, 2013. "Distributional vs. Quantile Regression," EIEF Working Papers Series 1329, Einaudi Institute for Economics and Finance (EIEF), revised Dec 2013.
    2. Holger Dette, 2013. "Comments on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(3), pages 437-441, September.
    3. Zhongjun Qu & Jungmo Yoon, 2011. "Nonparametric Estimation and Inference on Conditional Quantile Processes," Boston University - Department of Economics - Working Papers Series WP2011-059, Boston University - Department of Economics.
    4. Sabine Schnabel & Paul Eilers, 2013. "Simultaneous estimation of quantile curves using quantile sheets," AStA Advances in Statistical Analysis, Springer, vol. 97(1), pages 77-87, January.
    5. Ilaria Lucrezia Amerise, 2013. "Weighted Non-Crossing Quantile Regressions," Working Papers 201308, Università della Calabria, Dipartimento di Economia, Statistica e Finanza (Ex Dipartimento di Economia e Statistica).

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