Original scientific paper

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

Mark Kelbert orcid.org/0000-0002-3952-2012 ; Higher School of Economics, National Research University, Moscow, RF; Department of Mathematics, Swansea University, Swansea, UK
Pavel Mozgunov ; Higher School of Economics, National Research University, Moscow, RF;Department of Mathematics and Statistics, Lancaster University, Lancaster, UK

Abstract

The paper considers a family of probability distributions depending on a parameter.
The goal is to derive the generalized versions of Cramér-Rao and Bhattacharyya inequalities for the weighted covariance matrix and of the Kullback inequality for the weighted Kullback distance, which are important objects themselves [9, 23, 28]. The asymptotic
forms of these inequalities for a particular family of probability distributions and for a particular class of continuous weight functions are given.

Keywords

weighted covariance matrix; weighted Fisher information; Cramér-Rao inequality; Bhattacharyya inequality; Kullback inequality

Hrčak ID:

176703

URI

https://hrcak.srce.hr/176703

Publication date:

4.4.2017.

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