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Non-crossing non-parametric estimates of quantile curves

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  • Holger Dette
  • Stanislav Volgushev

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.

Suggested Citation

  • Holger Dette & Stanislav Volgushev, 2008. "Non-crossing non-parametric estimates of quantile curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 609-627.
  • Handle: RePEc:bla:jorssb:v:70:y:2008:i:3:p:609-627
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    References listed on IDEAS

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    1. Victor Chernozhukov & Iv·n Fern·ndez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves Without Crossing," Econometrica, Econometric Society, vol. 78(3), pages 1093-1125, May.
    2. Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Improving estimates of monotone functions by rearrangement," CeMMAP working papers CWP09/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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    Cited by:

    1. Qu, Zhongjun & Yoon, Jungmo, 2015. "Nonparametric estimation and inference on conditional quantile processes," Journal of Econometrics, Elsevier, vol. 185(1), pages 1-19.
    2. Samantha Leorato & Franco Peracchi, 2015. "Comparing Distribution and Quantile Regression," EIEF Working Papers Series 1511, Einaudi Institute for Economics and Finance (EIEF), revised Oct 2015.
    3. repec:eee:jmvana:v:164:y:2018:i:c:p:54-64 is not listed on IDEAS
    4. Fan, Yanqin & Liu, Ruixuan, 2016. "A direct approach to inference in nonparametric and semiparametric quantile models," Journal of Econometrics, Elsevier, vol. 191(1), pages 196-216.
    5. Liwen Zhang & Huixia Judy Wang & Zhongyi Zhu, 2017. "Composite change point estimation for bent line quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 145-168, February.
    6. Lian, Heng & Meng, Jie & Fan, Zengyan, 2015. "Simultaneous estimation of linear conditional quantiles with penalized splines," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 1-21.
    7. repec:gam:jrisks:v:5:y:2017:i:3:p:38-:d:105140 is not listed on IDEAS
    8. Angela Noufaily & M. C. Jones, 2013. "Parametric quantile regression based on the generalized gamma distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(5), pages 723-740, November.
    9. Shih-Kang Chao & Wolfgang K. Härdle & Ming Yuan, 2016. "Factorisable Multi-Task Quantile Regression," SFB 649 Discussion Papers SFB649DP2016-057, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    10. Karthik Sriram & R. V. Ramamoorthi & Pulak Ghosh, 2016. "On Bayesian Quantile Regression Using a Pseudo-joint Asymmetric Laplace Likelihood," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(1), pages 87-104, February.
    11. Franco Peracchi & Samantha Leorato, 2015. "Shape Regressions," Working Papers gueconwpa~15-15-06, Georgetown University, Department of Economics.
    12. Yuzhi Cai, 2016. "A Comparative Study Of Monotone Quantile Regression Methods For Financial Returns," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-16, May.
    13. Holger Dette & Matthias Guhlich & Natalie Neumeyer, 2015. "Testing for additivity in nonparametric quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(3), pages 437-477, June.
    14. 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.
    15. Sabine Schnabel & Paul Eilers, 2013. "Simultaneous estimation of quantile curves using quantile sheets," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(1), pages 77-87, January.
    16. Möst Lisa & Hothorn Torsten, 2015. "Conditional Transformation Models for Survivor Function Estimation," The International Journal of Biostatistics, De Gruyter, vol. 11(1), pages 23-50, May.
    17. 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;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 437-441, September.
    18. Ilaria Lucrezia Amerise, 2013. "Weighted Non-Crossing Quantile Regressions," Working Papers 201308, Università della Calabria, Dipartimento di Economia, Statistica e Finanza "Giovanni Anania" - DESF.
    19. Philippe Van Kerm & Seunghee Yu & Chung Choe, 2016. "Decomposing quantile wage gaps: a conditional likelihood approach," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(4), pages 507-527, August.

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