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Expectiles and M-quantiles are quantiles

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  • Jones, M. C.

Abstract

Expectiles and M-quantiles are related to means and M-estimates of location in the same way as quantiles are related to the median. We show that expectiles and certain M-quantiles of a distribution F are precisely the ordinary quantiles of distributions G related by an explicit formula to F.

Suggested Citation

  • Jones, M. C., 1994. "Expectiles and M-quantiles are quantiles," Statistics & Probability Letters, Elsevier, vol. 20(2), pages 149-153, May.
  • Handle: RePEc:eee:stapro:v:20:y:1994:i:2:p:149-153
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    Cited by:

    1. Hamidi, Benjamin & Maillet, Bertrand & Prigent, Jean-Luc, 2014. "A dynamic autoregressive expectile for time-invariant portfolio protection strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 46(C), pages 1-29.
    2. Genya Kobayashi, 2016. "Skew exponential power stochastic volatility model for analysis of skewness, non-normal tails, quantiles and expectiles," Computational Statistics, Springer, vol. 31(1), pages 49-88, March.
    3. Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2017. "Extreme M-quantiles as risk measures: From L1 to Lp optimization," TSE Working Papers 17-841, Toulouse School of Economics (TSE).
    4. Stephan Stahlschmidt & Matthias Eckardt & Wolfgang K. Härdle, 2014. "Expectile Treatment Effects: An efficient alternative to compute the distribution of treatment effects," SFB 649 Discussion Papers SFB649DP2014-059, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Philipp Gschöpf & Wolfgang Karl Härdle & Andrija Mihoci, 2015. "TERES - Tail Event Risk Expectile based Shortfall," SFB 649 Discussion Papers SFB649DP2015-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. V. Masson & N. Sim & L. Wedding, 2014. "Did the AFL equalization policy achieve the evenness of the league?," Applied Economics, Taylor & Francis Journals, vol. 46(35), pages 4334-4344, December.
    7. Paolo Radaelli & Michele Zenga, 2008. "Quantity quantiles linear regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(4), pages 455-469, October.
    8. Bellini, Fabio & Klar, Bernhard & Müller, Alfred & Rosazza Gianin, Emanuela, 2014. "Generalized quantiles as risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 41-48.
    9. repec:bla:jorssb:v:80:y:2018:i:2:p:263-292 is not listed on IDEAS
    10. Bellini, Fabio, 2012. "Isotonicity properties of generalized quantiles," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2017-2024.
    11. Borgini, Riccardo & Bianco, Paola Del & Salvati, Nicola & Schmid, Timo & Tzavidis, Nikos, 2015. "Modelling the distribution of health related quality of life of advanced melanoma patients in a longitudinal multi-centre clinical trial using M-quantile random effects regression," Discussion Papers 2015/19, Free University Berlin, School of Business & Economics.
    12. Giorgi, Emanuele & McNeil, Alexander J., 2016. "On the computation of multivariate scenario sets for the skew-t and generalized hyperbolic families," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 205-220.
    13. Abdelaati Daouia & Stéphane Girard & Gilles Stupfler, 2018. "Estimation of tail risk based on extreme expectiles," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(2), pages 263-292, March.
    14. Shih-Kang Chao & Katharina Proksch & Holger Dette & Wolfgang Karl Härdle, 2017. "Confidence Corridors for Multivariate Generalized Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 70-85, January.
    15. Xiu Xu & Andrija Mihoci & Wolfgang Karl Härdle, "undated". "lCARE – localizing Conditional AutoRegressive Expectiles," SFB 649 Discussion Papers SFB649DP2015-052, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    16. repec:spr:compst:v:33:y:2018:i:1:d:10.1007_s00180-017-0741-3 is not listed on IDEAS
    17. Mengmeng Guo & Wolfgang Härdle, 2012. "Simultaneous confidence bands for expectile functions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(4), pages 517-541, October.

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    Keywords

    Asymmetric loss M-estimation;

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