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Setwise independence for some dependence structures

Author

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  • Block, Henry W.
  • Fang, Zhaoben

Abstract

Characterization problems of setwise independence are considered by introducing the setwise dependence class SMk(n). Two questions are answered: 1. (i) Under which conditions is a strongly positive orthant dependent random vector setwise independent.2. (ii) Under what kind of dependence structure does a block diagonal covariance matrix imply setwise independence. The techniques involved in dealing with the above questions allow us to answer some open problems involving the SPOD class raised in Newman (1984, Inequalities in Statistics and Probability. IMS Lecture Notes--Monograph Series 5, pp. 127-140. IMS, Hayward, CA).

Suggested Citation

  • Block, Henry W. & Fang, Zhaoben, 1990. "Setwise independence for some dependence structures," Journal of Multivariate Analysis, Elsevier, vol. 32(1), pages 103-119, January.
    • Handle: RePEc:eee:jmvana:v:32:y:1990:i:1:p:103-119
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    Cited by:

    1. Li, Haijun & Scarsini, Marco & Shaked, Moshe, 1999. "Dynamic Linkages for Multivariate Distributions with Given Nonoverlapping Multivariate Marginals," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 54-77, January.
    2. Hu, Taizhong & Hu, Jinjin, 1998. "Comparison of order statistics between dependent and independent random variables," Statistics & Probability Letters, Elsevier, vol. 37(1), pages 1-6, January.
    3. Rudy Ligtvoet, 2022. "Incomplete Tests of Conditional Association for the Assessment of Model Assumptions," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1214-1237, December.
    4. Hu, Taizhong & Xie, Chaode & Ruan, Lingyan, 2005. "Dependence structures of multivariate Bernoulli random vectors," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 172-195, May.

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