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Theory of Probability and Mathematical Statistics

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Stein–Haff identity for the exponential family


Author: G. Alfelt
Journal: Theor. Probability and Math. Statist. 99 (2019), 5-17
MSC (2010): Primary 62H12; Secondary 62C99
DOI: https://doi.org/10.1090/tpms/1076
Published electronically: February 27, 2020
MathSciNet review: 3908652
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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.


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Additional Information

G. Alfelt
Affiliation: Department of Mathematics, Stockholm University, Roslagsvägen 101, SE-10691 Stockholm, Sweden
Email: gustava@math.su.se

Keywords: Random matrices, matrix-variate gamma distribution, decision theory
Received by editor(s): June 21, 2018
Published electronically: February 27, 2020
Article copyright: © Copyright 2020 American Mathematical Society