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Dependence structures of multivariate Bernoulli random vectors

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  • Hu, Taizhong
  • Xie, Chaode
  • Ruan, Lingyan

Abstract

In some situations, it is difficult and tedious to check notions of dependence properties and dependence orders for multivariate distributions supported on a finite lattice. The purpose of this paper is to utilize a newly developed tool, majorization with respect to weighted trees, to lay out some general results that can be used to identify some dependence properties and dependence orders for multivariate Bernoulli random vectors. Such a study gives us some new insight into the relations between the concepts of dependence.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:94:y:2005:i:1:p:172-195
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    References listed on IDEAS

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    1. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
    2. Susan H. Xu & Haijun Li, 2000. "Majorization of Weighted Trees: A New Tool to Study Correlated Stochastic Systems," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 298-323, May.
    3. Müller, Alfred & Scarsini, Marco, 2000. "Some Remarks on the Supermodular Order," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 107-119, April.
    4. Block, Henry W. & Fang, Zhaoben, 1990. "Setwise independence for some dependence structures," Journal of Multivariate Analysis, Elsevier, vol. 32(1), pages 103-119, January.
    5. Susan H. Xu, 1999. "Structural Analysis of a Queueing System with Multiclasses of Correlated Arrivals and Blocking," Operations Research, INFORMS, vol. 47(2), pages 264-276, April.
    6. Allan R. Sampson & Lyn R. Whitaker, 1988. "Positive Dependence, Upper Sets, and Multidimensional Partitions," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 254-264, May.
    7. Christofides, Tasos C. & Vaggelatou, Eutichia, 2004. "A connection between supermodular ordering and positive/negative association," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 138-151, January.
    8. Frostig, Esther, 2001. "Comparison of portfolios which depend on multivariate Bernoulli random variables with fixed marginals," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 319-332, December.
    9. Shaked, Moshe & Shanthikumar, J. George, 1997. "Supermodular Stochastic Orders and Positive Dependence of Random Vectors," Journal of Multivariate Analysis, Elsevier, vol. 61(1), pages 86-101, April.
    10. Frostig, Esther, 2003. "Ordering ruin probabilities for dependent claim streams," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 93-114, February.
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    Cited by:

    1. Margaret Meyer & Bruno Strulovici, 2013. "The Supermodular Stochastic Ordering," Discussion Papers 1563, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Meyer, Margaret & Strulovici, Bruno, 2012. "Increasing interdependence of multivariate distributions," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1460-1489.
    3. Xuejun Wang & Yi Wu & Shuhe Hu, 2018. "Strong and weak consistency of LS estimators in the EV regression model with negatively superadditive-dependent errors," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(1), pages 41-65, January.
    4. Xuejun Wang & Aiting Shen & Zhiyong Chen & Shuhe Hu, 2015. "Complete convergence for weighted sums of NSD random variables and its application in the EV regression model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 166-184, March.
    5. Li, Chen & Li, Xiaohu, 2019. "Preservation of WSAI under default transforms and its application in allocating assets with dependent realizable returns," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 84-91.

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