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Isotonicity properties of generalized quantiles

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  • Bellini, Fabio
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    Abstract

    We investigate whether several families of generalized quantiles (expectiles, Lp-quantiles and M-quantiles) respect various stochastic orders (the usual stochastic order, the convexity order, and the p-convexity orders).

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 11 ()
    Pages: 2017-2024

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:11:p:2017-2024

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    Related research

    Keywords: Expectiles; Generalized quantiles; Stochastic orders; Isotonicity; Submodularity;

    References

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    1. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521608275, October.
    2. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    3. Bellini, Fabio & Rosazza Gianin, Emanuela, 2012. "Haezendonck–Goovaerts risk measures and Orlicz quantiles," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 107-114.
    4. Jones, M. C., 1994. "Expectiles and M-quantiles are quantiles," Statistics & Probability Letters, Elsevier, vol. 20(2), pages 149-153, May.
    5. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-47, July.
    6. Koenker, Roger, 1992. "When Are Expectiles Percentiles?," Econometric Theory, Cambridge University Press, vol. 8(03), pages 423-424, September.
    7. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
    8. Chen, Zehua, 1996. "Conditional Lp-quantiles and their application to the testing of symmetry in non-parametric regression," Statistics & Probability Letters, Elsevier, vol. 29(2), pages 107-115, August.
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