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

Mark Kelbert; Pavel Mozgunov

Vol. 22 No. 1 (2017)

Regular Articles

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

Published 2016-07-13

Mark Kelbert
Pavel Mozgunov

Mark Kelbert
National Research University Higher School of Economics, Moscow, Russia; Swansea University, Swansea, UK

Pavel Mozgunov
National Research University Higher School of Economics, Moscow, Russia; Lancaster University, Lancaster, UK

Submission of an original manuscript to the Mathematical Communications will be taken to mean that it represents original work not previously published, that it is not being considered elsewhere for publication; and, if accepted for publication, it will be published in print and online form and it will not be published elsewhere in the same form, for commercial purposes, in any language, without the consent of the publisher. The journal takes the stance that the publication of scholarly research is meant to disseminate knowledge and, in a not-for-profit regime, benefits neither publisher nor author financially. It sees itself as having an obligation to its authors and to society to make content available online now that the technology allows for such a possibility.

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

PDF

Supplementary File(s)

LaTeX file