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Covariance matrix inequalities for functions of Beta random variables

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  • Wei, Zhengyuan
  • Zhang, Xinsheng

Abstract

Based on Jacobi polynomial series expansion and some innovative definitions of high-order differential matrix, we derive lower and upper bounds on covariance matrix for multivariate functions of Beta random variables in the sense of Loewner ordering for matrices. Additionally, corresponding univariate results obtained conveniently along the line of our arguments.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:7:p:873-879
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    References listed on IDEAS

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    1. Chen, Louis H. Y., 1982. "An inequality for the multivariate normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 12(2), pages 306-315, June.
    2. Liu, Jun S., 1994. "Siegel's formula via Stein's identities," Statistics & Probability Letters, Elsevier, vol. 21(3), pages 247-251, October.
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    Cited by:

    1. Giorgos Afendras & Vassilis Papathanasiou, 2014. "A note on a variance bound for the multinomial and the negative multinomial distribution," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(3), pages 179-183, April.
    2. Giorgos Afendras, 2013. "Unified extension of variance bounds for integrated Pearson family," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 687-702, August.

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