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Research output: Contribution to Journal/Magazine › Journal article › peer-review

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**Generalization of Cramér-Rao and Bhattacharyya inequalities for the weighted covariance matrix.** / Kelbert, Mark; Mozgunov, Pavel.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Kelbert, M & Mozgunov, P 2017, 'Generalization of Cramér-Rao and Bhattacharyya inequalities for the weighted covariance matrix', *Mathematical Communications*, vol. 22, no. 1, pp. 25-40. <http://www.mathos.unios.hr/mc/index.php/mc/article/view/1634>

Kelbert, M., & Mozgunov, P. (2017). Generalization of Cramér-Rao and Bhattacharyya inequalities for the weighted covariance matrix. *Mathematical Communications*, *22*(1), 25-40. http://www.mathos.unios.hr/mc/index.php/mc/article/view/1634

Kelbert M, Mozgunov P. Generalization of Cramér-Rao and Bhattacharyya inequalities for the weighted covariance matrix. Mathematical Communications. 2017 Jun 1;22(1):25-40.

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title = "Generalization of Cram{\'e}r-Rao and Bhattacharyya inequalities for the weighted covariance matrix",

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.",

keywords = "weighted covariance matrix, weighted Fisher information, Rao-Cramer inequality, Bhattacharyya inequality, Kullback inequality",

author = "Mark Kelbert and Pavel Mozgunov",

year = "2017",

month = jun,

day = "1",

language = "English",

volume = "22",

pages = "25--40",

journal = "Mathematical Communications",

issn = "1331-0623",

publisher = "Udruga Matematicara Osijek",

number = "1",

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TY - JOUR

T1 - Generalization of Cramér-Rao and Bhattacharyya inequalities for the weighted covariance matrix

AU - Kelbert, Mark

AU - Mozgunov, Pavel

PY - 2017/6/1

Y1 - 2017/6/1

N2 - 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.

AB - 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.

KW - weighted covariance matrix

KW - weighted Fisher information

KW - Rao-Cramer inequality

KW - Bhattacharyya inequality

KW - Kullback inequality

M3 - Journal article

VL - 22

SP - 25

EP - 40

JO - Mathematical Communications

JF - Mathematical Communications

SN - 1331-0623

IS - 1

ER -