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

Sa？etak 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