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A note on conditional covariance matrices for elliptical distributions

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  • Jaworski, Piotr
  • Pitera, Marcin

Abstract

In this short note we provide an analytical formula for the conditional covariance matrices of the elliptically distributed random vectors, when the conditioning is based on the values of any linear combination of the marginal random variables. We show that one could introduce the univariate invariant depending solely on the conditioning set, which greatly simplifies the calculations.

Suggested Citation

  • Jaworski, Piotr & Pitera, Marcin, 2017. "A note on conditional covariance matrices for elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 230-235.
    • Handle: RePEc:eee:stapro:v:129:y:2017:i:c:p:230-235
    DOI: 10.1016/j.spl.2017.06.003
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    References listed on IDEAS

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    1. Furman, Edward & Landsman, Zinoviy, 2006. "Tail Variance Premium with Applications for Elliptical Portfolio of Risks," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 433-462, November.
    2. Zinoviy Landsman & Emiliano Valdez, 2003. "Tail Conditional Expectations for Elliptical Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 55-71.
    3. 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.
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    Cited by:

    1. Damian Jelito & Marcin Pitera, 2018. "New fat-tail normality test based on conditional second moments with applications to finance," Papers 1811.05464, arXiv.org, revised Apr 2020.
    2. Jaworski, Piotr & Pitera, Marcin, 2020. "A note on conditional variance and characterization of probability distributions," Statistics & Probability Letters, Elsevier, vol. 163(C).
    3. Damian Jelito & Marcin Pitera, 2021. "New fat-tail normality test based on conditional second moments with applications to finance," Statistical Papers, Springer, vol. 62(5), pages 2083-2108, October.

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