Gelfand pairs and zonal polynomials in Multivariate Statistical Analysis

Mauro Pagliacci

No 0003/2014, Working papers of the Department of Economics - University of Perugia (IT) from Università di Perugia, Dipartimento Economia

Abstract: 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.

Keywords: Gelfand pairs; spherical functions; zonal polynomials; non-central Wishart distribution. (search for similar items in EconPapers)
Pages: 27 pages
Date: 2014-11-03
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