Generalization of Cramér-Rao and Bhattacharyya inequalities for the weighted covariance matrix

Mark Kelbert, Pavel Mozgunov

Abstract


The paper considers a family of probability distribution depending on a parameter. The goal is to derive the generalized versions of Rao-Cramer, Bhattacharyya inequalities for the weighted covariance matrix and of the Kullback inequality for the weighted Kullback distance which are important objects themselves. The asymptotic forms of these inequalities for a particular family of probability distribution and for a particular class of weight functions are given.

Keywords


weighted covariance matrix, weighted Fisher information, Rao-Cram\'er inequality, Bhattacharyya inequality, Kullback inequality

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ISSN: 1331-0623 (Print), 1848-8013 (Online)