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A distance between elliptical distributions based in an embedding into the Siegel group. (English) Zbl 1021.62041

Summary: This paper describes two different embeddings of the manifolds corresponding to many elliptical probability distributions with the informative geometry into the manifold of positive-definite matrices with the Siegel metric, generalizing a result published previously elsewhere. These new general embeddings are applicable to a wide class of elliptical probability distributions, in which the normal, \(t\)-Student and Cauchy are specific examples. A lower bound for the Rao distance is obtained, which is itself a distance, and, through these embeddings, a number of statistical tests of hypotheses are derived.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H15 Hypothesis testing in multivariate analysis
62A01 Foundations and philosophical topics in statistics
11F99 Discontinuous groups and automorphic forms
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