The Annals of Probability

Moment Bounds for Associated Sequences

Thomas Birkel

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Abstract

Let $\{X_j: j \in \mathbb{N}\}$ be a sequence of associated random variables with zero mean and let $r > 2$. We give two conditions--on the moments and on the covariance structure of the process--which guarantee that $\sup_{m \in \mathbb{N} \cup \{0\}} E| \sum^{m+n}_{j=m+1} X_j|^r = O(n^{r/2})$ holds. Examples show that neither condition can be weakened.

Article information

Source
Ann. Probab., Volume 16, Number 3 (1988), 1184-1193.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991684

Digital Object Identifier
doi:10.1214/aop/1176991684

Mathematical Reviews number (MathSciNet)
MR942762

Zentralblatt MATH identifier
0647.60039

JSTOR
links.jstor.org

Subjects
Primary: 60E15: Inequalities; stochastic orderings
Secondary: 62H20: Measures of association (correlation, canonical correlation, etc.)

Keywords
Moment bounds partial sums of associated random variables

Citation

Birkel, Thomas. Moment Bounds for Associated Sequences. Ann. Probab. 16 (1988), no. 3, 1184--1193. doi:10.1214/aop/1176991684. https://projecteuclid.org/euclid.aop/1176991684


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