The essential dependence for a group of random vectors

Lingyue Zhang, Dawei Lu and Xiaoguang Wang

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 24, 5836-5872

Abstract: Considering random variables Xi,i=1,2,…,n which are from dominated distributions, we divide them into {X(1),…,X(m)},m≤n, where X(j),j=1,…,m are random vectors. Inspired by copula and Kullback-Leibler divergence, by extending probability density function to Radon-Nikodym derivative w.r.t. a σ-finite product measure, the amount DivM(X(1),…,X(m)) is proposed with some desirable properties to describe the essential dependence for that group of random vectors. Some examples are given to demonstrate the amount can be applied to describe the essential dependence under both continuous and discrete distributions and can capture the associations such as MTP2, POD.

Date: 2021
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DOI: 10.1080/03610926.2020.1737128

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