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Characterization of the Jørgensen set in generalized linear models. (English) Zbl 0815.62030

Summary: D. N. Shanbhag’s [Aust. J. Stat. 30A, Spec. Issue, 272-280 (1988; Zbl 0694.62024)] clever method for finding the Jørgensen set [B. Jørgensen, J. R. Stat. Soc., Ser. B 49, 127-162 (1987; Zbl 0662.62078)] of the family of Wishart distributions on symmetric matrices is extended here to Wishart distributions on symmetric cones, such as Hermitian matrices on complex numbers or quaternions. The idea is also extended to various other multivariate distributions, including the natural exponential family associated with the set of normal distributions on \(R\) with unknown mean and variance.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62J12 Generalized linear models (logistic models)
60E99 Distribution theory
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