ISSN 2234-8417 (Online) ISSN 1598-5857 (Print)

 2012's 30,3-4(May)

 On H$\grave{a}$jek-R$\grave{e}$nyi-type inequality for conditionally negatively associated random variables and its applications By HYE-YOUNG SEO ..........1339

Generic Number - 1339
References - 0
Written Date - May 15th, 12
Modified Date - May 15th, 12
Visited Counts - 791

Original File
 Summary Let $\{ \Omega, \mathcal{F}, P \}$ be a probability space and $\{X_n | n \geq 1\}$ be a sequence of random variables defined on it. A finite sequence of random variables $\{X_n | n \geq 1\}$ is said to be conditionally negatively associated given $\mathcal{F}$ if for every pair of disjoint subsets $A$ and $B$ of $\{ 1, 2, \cdots, n \},$ $Cov^{\mathcal{F}} (f_1 (X_i , i \in A), f_2 (X_j , j \in B))\leq 0 ~a.s.$ whenever $f_1$ and $f_2$ are coordinatewise nondecreasing functions. We extend the H$\grave {a}$jek-R$\grave{e}$nyi-type inequality from negative association to conditional negative association of random variables. In addition, some corollaries are given.

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http://www.springer.com/journal/12190
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