A note on some negative dependence notions |
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Authors: | Tae-Sung Kim Hye-Young Seo |
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Institution: | Department of Statistics , WonKwang University , 344-2, Shinyong-Dong, Chollabuk-Do, Iri(570-749), REPUBLIC OF KOREA |
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Abstract: | A random vector X = (X 1,…,X n ) is negatively associated if and only if for every pair of partitions X 1 = (X π(1),…,X π(k)), X 2 = (X π(k+1),…,X π(n)) of X , P( X 1 ? A, X 2 ? B) ≤ P( X 1 ? A)P( X 2 ? B) whenever A and B are open upper sets and π is any permutation of {1,…,n}. In this paper, we develop some of concepts of negative dependence, which are weaker than negative association but stronger than negative orthant dependence by requiring the above inequality to hold only for some upper sets A and B and applying the arguments in Shaked. |
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Keywords: | Negative association Negative dependence Negative orthant dependence Upper sets Central limit theorem |
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