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

Kelbert, Mark and Mozgunov, Pavel (2017) Generalization of Cramér-Rao and Bhattacharyya inequalities for the weighted covariance matrix. Mathematical Communications, 22 (1). pp. 25-40. ISSN 1331-0623

Abstract

The paper considers a family of probability distributions depending on a parameter. The goal is to derive the generalized versions of Cramer-Rao and 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 distributions and for a particular class of continuous weight functions are given.