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A distance between multivariate normal distributions based in an embedding into the Siegel group. (English) Zbl 0719.62062

The authors define an embedding of the manifold of multivariate normal densities with the informative geometry into the manifold of positive definite matrices with the Siegel metric. In this way they obtain a lower bound for the Rao distance. They give applications to hypotheses testing and data analysis based on this new distance.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62B10 Statistical aspects of information-theoretic topics
62H30 Classification and discrimination; cluster analysis (statistical aspects)
53C40 Global submanifolds
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