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Stochastic orderings for elliptical random vectors

Author

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  • Pan, Xiaoqing
  • Qiu, Guoxin
  • Hu, Taizhong

Abstract

The authors provide sufficient and/or necessary conditions for classifying multivariate elliptical random vectors according to the convex ordering and the increasing convex ordering. Their results generalize the corresponding ones for multivariate normal random vectors in the literature.

Suggested Citation

  • Pan, Xiaoqing & Qiu, Guoxin & Hu, Taizhong, 2016. "Stochastic orderings for elliptical random vectors," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 83-88.
    • Handle: RePEc:eee:jmvana:v:148:y:2016:i:c:p:83-88
    DOI: 10.1016/j.jmva.2016.02.016
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    References listed on IDEAS

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    1. Marco Scarsini & Alessandro Arlotto, 2009. "Hessian orders and multinormal distributions - à paraître," Post-Print hal-00542400, HAL.
    2. Landsman, Zinoviy & Tsanakas, Andreas, 2006. "Stochastic ordering of bivariate elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 488-494, March.
    3. Marco Scarsini, 1998. "Multivariate convex orderings, dependence, and stochastic equality," Post-Print hal-00541775, HAL.
    4. Ding, Ying & Zhang, Xinsheng, 2004. "Some stochastic orders of Kotz-type distributions," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 389-396, October.
    5. Block, Henry W. & Sampson, Allan R., 1988. "Conditionally ordered distributions," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 91-104, October.
    6. Arlotto, Alessandro & Scarsini, Marco, 2009. "Hessian orders and multinormal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2324-2330, November.
    7. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    8. Alfred Müller, 2001. "Stochastic Ordering of Multivariate Normal Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 567-575, September.
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    Cited by:

    1. Amiri, Mehdi & Izadkhah, Salman & Jamalizadeh, Ahad, 2020. "Linear orderings of the scale mixtures of the multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    2. Mehdi Amiri & Narayanaswamy Balakrishnan & Abbas Eftekharian, 2022. "Hessian orderings of multivariate normal variance-mean mixture distributions and their applications in evaluating dependent multivariate risk portfolios," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(3), pages 679-707, September.
    3. Rüschendorf Ludger & Witting Julian, 2017. "VaR bounds in models with partial dependence information on subgroups," Dependence Modeling, De Gruyter, vol. 5(1), pages 59-74, January.
    4. Chuancun Yin, 2019. "Stochastic Orderings of Multivariate Elliptical Distributions," Papers 1910.07158, arXiv.org, revised Nov 2019.

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