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ISSN 2385-2275 No. 3 - November 2014

Gelfand pairs and zonal polynomials in Multivariate Statistical Analysis

University of Perugia, Department of Economics, Perugia, Italy Questo indirizzo email è protetto dagli spambots. È necessario abilitare JavaScript per vederlo.


This article shows how Harmonic Analysis on matrix groups can solve specifc problems of Multivariate Statistical Analysis. In particular are studied the properties of zonal polynomials, seen as spherical functions of a classical Gelfand pair. A duality formula allows to write the zonal polynomials as spherical functions of a finite Gelfand pair. Finally a combinatorial technique for the calculation of the zonal polynomials shows that these are the analogous, in the non-central Wishart distribution, of power in central Wishart distribution.


A.M.S. Mathematics Subject Classification (1985): 62A10, 43A90, 43A80

Keywords: Gelfand pairs, spherical functions, zonal polynomials, non-central Wishart distribution



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