[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5351/CKSS.2011.18.6.799

On the Hàjek-Rènyi-Type Inequality for Conditionally Associated Random Variables

Choi, Jeong-Yeol (School of Mathematics and Informational Statistics, Wonkwang University)
Seo, Hye-Young (School of Mathematics and Informational Statistics, Wonkwang University)
Baek, Jong-Il (School of Mathematics and Informational Statistics, Wonkwang University)

Publication Information

Communications for Statistical Applications and Methods / v.18, no.6, 2011 , pp. 799-808 More about this Journal

Abstract

Let { ${\Omega}$ , $\mathcal{F}$ , P} be a probability space and { $X_n{\mid}n{\geq}1$ } be a sequence of random variables defined on it. A finite sequence of random variables { $X_i{\mid}1{\leq}i{\leq}n$ } is a conditional associated given $\mathcal{F}$ if for any coordinate-wise nondecreasing functions f and g defined on $R^n$ , $Cov^{\mathcal{F}}$ (f( $X_1$ , ${\ldots}$ , $X_n$ ), g( $X_1$ , ${\ldots}$ , $X_n$ )) ${\geq}$ 0 a.s. whenever the conditional covariance exists. We obtain the H $\grave{a}$ jek-R $\grave{e}$ nyi-type inequality for conditional associated random variables. In addition, we establish the strong law of large numbers, the three series theorem, integrability of supremum, and a strong growth rate for $\mathcal{F}$ -associated random variables.

Keywords

Associated random variables; conditional covariance; conditional associated random variables; H $\grave{a}$ jek-R $\grave{e}$ nyi-type inequality;

Citations & Related Records

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