Theory of Probability and Mathematical Statistics
Stein‒Haff identity for the exponential family
G. Alfelt
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Abstract: In this paper, the Stein–Haff identity is established for positive-definite and symmetric random matrices belonging to the exponential family. The identity is then applied to the matrix-variate gamma distribution, and an estimator that dominates the maximum likelihood estimator in terms of Stein’s loss is obtained. Finally, a simulation study is conducted in order to support the theoretical results.
Keywords: Random matrices, matrix-variate gamma distribution, decision theory.
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