Hierarchical orbital decompositions and extended decomposable distributions

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dc.creatorKamiya, Hidehiko
dc.creatorTakemura, Akimichi
dc.date2006-06-23
dc.date.accessioned2026-07-07T08:56:18Z
dc.date.available2026-07-07T08:56:18Z
dc.descriptionElliptically contoured distributions can be considered to be the distributions for which the contours of the density functions are proportional ellipsoids. Kamiya, Takemura and Kuriki (2006) generalized the elliptically contoured distributions to star-shaped distributions, for which the contours are allowed to be arbitrary proportional star-shaped sets. This was achieved by considering the so-called orbital decomposition of the sample space in the general framework of group invariance. In the present paper, we extend their results by conducting the orbital decompositions in steps and obtaining a further, hierarchical decomposition of the sample space. This allows us to construct probability models and distributions with further independence structures. The general results are applied to the star-shaped distributions with a certain symmetric structure, the distributions related to the two-sample Wishart problem and the distributions of preference rankings.
dc.identifierhttps://arxiv.org/abs/math/0606576
dc.identifierhttp://arxiv.org/abs/math/0606576
dc.identifierJournal of Multivariate Analysis, Vol.99, 2008, 339-357
dc.identifierdoi:10.1016/j.jmva.2006.09.010
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146564
dc.subjectStatistics Theory
dc.subject62H10
dc.titleHierarchical orbital decompositions and extended decomposable distributions
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