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A generalization of the Wishart distribution for the elliptical model and its moments for the multivariate t model

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  • Sutradhar, Brajendra C.
  • Ali, Mir M.

Abstract

We consider the elliptical distribution of n p-dimensional random vectors X1, ..., Xn having p.d.f. of the form k(n, p) [Lambda]-n/2 g([Sigma]j=1n(Xj-[theta])' [Lambda]-1(Xj-[theta])) as a generalization of the multivariate normal distribution. Let A denote the Wishart matrix defined by , where the vector is given by . In this paper we derive the distribution of A when X1, ..., Xn is assumed to have an elliptical distribution. This result is specialized to the case where X1, ..., Xn is assumed to have a multivariate t distribution, a subclass of the elliptical class of distributions. Furthermore, the first two moments of A for this subclass is computed.

Suggested Citation

  • Sutradhar, Brajendra C. & Ali, Mir M., 1989. "A generalization of the Wishart distribution for the elliptical model and its moments for the multivariate t model," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 155-162, April.
    • Handle: RePEc:eee:jmvana:v:29:y:1989:i:1:p:155-162
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    Citations

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    Cited by:

    1. Fang, B.Q., 2008. "Noncentral matrix quadratic forms of the skew elliptical variables," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1105-1127, July.
    2. Kibria, B. M. Golam & Haq, M. Safiul, 1999. "Predictive Inference for the Elliptical Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 235-249, February.
    3. Bodnar, Olha & Bodnar, Taras, 2021. "Objective Bayesian meta-analysis based on generalized multivariate random effects model," Working Papers 2021:5, Örebro University, School of Business.
    4. Kibria, B.M. Golam, 2006. "The matrix-t distribution and its applications in predictive inference," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 785-795, March.
    5. Guo, Junhao & Zhou, Jie & Hu, Sanfeng, 2020. "Intrinsic covariance matrix estimation for multivariate elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 162(C).
    6. Brajendra C. Sutradhar, 2022. "Fixed versus Mixed Effects Based Marginal Models for Clustered Correlated Binary Data: an Overview on Advances and Challenges," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 259-302, May.
    7. Bekker, Andriëtte & van Niekerk, Janet & Arashi, Mohammad, 2017. "Wishart distributions: Advances in theory with Bayesian application," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 272-283.
    8. Micheas, Athanasios C. & Dey, Dipak K., 2005. "Modeling shape distributions and inferences for assessing differences in shapes," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 257-280, February.
    9. Fang, B.Q., 2006. "Sample mean, covariance and T2 statistic of the skew elliptical model," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1675-1690, August.
    10. Ogasawara, Haruhiko, 2023. "The density of the sample correlations under elliptical symmetry with or without the truncated variance-ratio," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    11. A. Batsidis & K. Zografos, 2006. "Discrimination of Observations into One of Two Elliptic Populations based on Monotone Training Samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(2), pages 221-241, October.

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