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Some Stein-type inequalities for multivariate elliptical distributions and applications

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  • Landsman, Zinoviy
  • Vanduffel, Steven
  • Yao, Jing

Abstract

Brown et al. (2006) derive a Stein-type inequality for the multivariate Student’s t-distribution. We generalize their result to the family of (multivariate) generalized hyperbolic distributions and derive a lower bound for the variance of a function of a random variable.

Suggested Citation

  • Landsman, Zinoviy & Vanduffel, Steven & Yao, Jing, 2015. "Some Stein-type inequalities for multivariate elliptical distributions and applications," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 54-62.
    • Handle: RePEc:eee:stapro:v:97:y:2015:i:c:p:54-62
    DOI: 10.1016/j.spl.2014.11.005
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    References listed on IDEAS

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    1. Landsman, Zinoviy, 2006. "On the generalization of Stein's Lemma for elliptical class of distributions," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 1012-1016, May.
    2. Cacoullos, T. & Papathanasiou, V., 1989. "Characterizations of distributions by variance bounds," Statistics & Probability Letters, Elsevier, vol. 7(5), pages 351-356, April.
    3. Christophe Ley & Yvik Swan, 2013. "Parametric Stein Operators and Variance Bounds," Working Papers ECARES ECARES 2013-28, ULB -- Universite Libre de Bruxelles.
    4. Vandendorpe, Antoine & Ho, Ngoc-Diep & Vanduffel, Steven & Van Dooren, Paul, 2008. "On the parameterization of the CreditRisk + model for estimating credit portfolio risk," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 736-745, April.
    5. Landsman, Zinoviy & Neslehová, Johanna, 2008. "Stein's Lemma for elliptical random vectors," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 912-927, May.
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    Cited by:

    1. Moawia Alghalith & Wing-Keung Wong, 2020. "Extension of Stein's Lemmas to General Functions and Distributions," Advances in Decision Sciences, Asia University, Taiwan, vol. 24(4), pages 77-88, December.
    2. Nitis Mukhopadhyay, 2021. "On Rereading Stein’s Lemma: Its Intrinsic Connection with Cramér-Rao Identity and Some New Identities," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 355-367, March.
    3. Shushi, Tomer, 2018. "Stein’s lemma for truncated elliptical random vectors," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 297-303.
    4. Moawia Alghalith & Wing-Keung Wong, 2020. "Extension of Stein's Lemmas to General Functions and Distributions," Advances in Decision Sciences, Asia University, Taiwan, vol. 24(4), pages 77-88, December.

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