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Regular version of the site

Article

Generalization of Cram´er-Rao and Bhattacharyya inequalities for the weighted covariance matrix

Mathematical Communications. 2017. Vol. 22. No. 1. P. 25-40.
Kelbert M., Mozgunov P.

The paper considers a family of probability distributions depending on a pa-
rameter. The goal is to derive the generalized versions of Cram´er-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 asymp-
totic forms of these inequalities for a particular family of probability distributions and for
a particular class of continuous weight functions are given.