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

- Journal title : Communications for Statistical Applications and Methods
- Volume 18, Issue 6, 2011, pp.799-808
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CKSS.2011.18.6.799

Title & Authors

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

Choi, Jeong-Yeol; Seo, Hye-Young; Baek, Jong-Il;

Choi, Jeong-Yeol; Seo, Hye-Young; Baek, Jong-Il;

Abstract

Let {, , P} be a probability space and {} be a sequence of random variables defined on it. A finite sequence of random variables {} is a conditional associated given if for any coordinate-wise nondecreasing functions f and g defined on , (f(, , ), g(, , )) 0 a.s. whenever the conditional covariance exists. We obtain the Hjek-Rnyi-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 -associated random variables.

Keywords

Associated random variables;conditional covariance;conditional associated random variables;Hjek-Rnyi-type inequality;

Language

English

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