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Siegel's formula via Stein's identities

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  • Liu, Jun S.

Abstract

Inspired by a surprising formula in Siegel (1993), we find it convenient to compute covariances, even for order statistics, by using Stein's (1972) identities. Generalizations of Siegel's formula to other order statistics as well as other distributions are obtained along this line.

Suggested Citation

  • Liu, Jun S., 1994. "Siegel's formula via Stein's identities," Statistics & Probability Letters, Elsevier, vol. 21(3), pages 247-251, October.
    • Handle: RePEc:eee:stapro:v:21:y:1994:i:3:p:247-251
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    Cited by:

    1. Ravi Kashyap, 2016. "The Perfect Marriage and Much More: Combining Dimension Reduction, Distance Measures and Covariance," Papers 1603.09060, arXiv.org, revised Jul 2019.
    2. Wei, Zhengyuan & Zhang, Xinsheng, 2009. "Covariance matrix inequalities for functions of Beta random variables," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 873-879, April.
    3. Shushi, Tomer, 2018. "Stein’s lemma for truncated elliptical random vectors," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 297-303.
    4. Kashyap, Ravi, 2019. "The perfect marriage and much more: Combining dimension reduction, distance measures and covariance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    5. H. Youn Kim & Keith R. McLaren & K.K. Gary Wong, 2014. "Consumer Demand, Consumption, and Asset Pricing: An Integrated Analysis," Monash Econometrics and Business Statistics Working Papers 4/14, Monash University, Department of Econometrics and Business Statistics.
    6. Vanduffel, Steven & Yao, Jing, 2017. "A stein type lemma for the multivariate generalized hyperbolic distribution," European Journal of Operational Research, Elsevier, vol. 261(2), pages 606-612.
    7. Vitale, Richard A., 1996. "Covariance identities for normal variables via convex polytopes," Statistics & Probability Letters, Elsevier, vol. 30(4), pages 363-368, November.
    8. C. Adcock, 2010. "Asset pricing and portfolio selection based on the multivariate extended skew-Student-t distribution," Annals of Operations Research, Springer, vol. 176(1), pages 221-234, April.
    9. Adcock, C.J., 2014. "Mean–variance–skewness efficient surfaces, Stein’s lemma and the multivariate extended skew-Student distribution," European Journal of Operational Research, Elsevier, vol. 234(2), pages 392-401.

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