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The essential dependence for a group of random vectors

Author

Listed:
  • Lingyue Zhang
  • Dawei Lu
  • Xiaoguang Wang

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.

Suggested Citation

  • Lingyue Zhang & Dawei Lu & Xiaoguang Wang, 2021. "The essential dependence for a group of random vectors," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(24), pages 5836-5872, November.
    • Handle: RePEc:taf:lstaxx:v:50:y:2021:i:24:p:5836-5872
    DOI: 10.1080/03610926.2020.1737128
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