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An identity for multivariate elliptically contoured matrix distribution

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  • Bodnar, Taras
  • Gupta, Arjun K.

Abstract

In this paper, we derive the Stein-Haff identity for the multivariate elliptically contoured matrix distributions. Our results generalize the results of the papers by [Stein, C., 1977. Personal communication. Unpublished notes on estimating the covariance matrix] and [Haff, L.R., 1979a. An identity for the Wishart distribution with applications. J. Multivariate Anal. 9, 531-542] for the much more general family of the matrix variate distributions. Moreover, we simplify the proof of the Stein-Haff identity given by [Kubokawa, T., Srivastava, M.S., 1999. Robust improvement in estimation of a covariance matrix in an elliptically contoured distribution. Ann. Statist. 27, 600-609] for the vector elliptically contoured matrix distribution in some important partial cases.

Suggested Citation

  • Bodnar, Taras & Gupta, Arjun K., 2009. "An identity for multivariate elliptically contoured matrix distribution," Statistics & Probability Letters, Elsevier, vol. 79(10), pages 1327-1330, May.
  • Handle: RePEc:eee:stapro:v:79:y:2009:i:10:p:1327-1330
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    1. Haff, L. R., 1979. "An identity for the Wishart distribution with applications," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 531-544, December.
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    1. Taras Bodnar & Arjun Gupta, 2013. "An exact test for a column of the covariance matrix based on a single observation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(6), pages 847-855, August.

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