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 Unpublished notes on estimating the covariance matrix] and [Haff, L.R., 1979a.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.
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