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Title: The Matsumoto-Yor property on trees for matrix variates of different dimensions Authors:  Konstancja Bobecka - Warsaw University of Technology (Poland) [presenting]
Abstract: The focus is on an extension of the multivariate Matsumoto-Yor (MY)independence property with respect to a tree with $p$ vertices to the case where random variables corresponding to the vertices of the tree are replaced by random matrices. The converse of the $p-$variate MY property, which characterizes the product of one gamma and $p - 1$ generalized inverse Gaussian distributions, is extended to characterize the product of the Wishart and $p - 1$ matrix generalized inverse Gaussian distributions.