Strong laws for associated random variables. Issue 6 (2nd November 2017)

• Record Type: Journal Article
• Authors: Çağın, Tonguç; Oliveira, Paulo Eduardo
• Is Part Of: Statistics. Volume 51:Issue 6(2017)
• Page Start: 1259
• Page End: 1279
• Publication Date: 2017-11-02
• Subjects: Almost sure convergence -- association -- convergence rates -- exponential inequalities -- Marcinkiewicz–Zygmund law; 60F15; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2017.1345907
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: We study the almost sure convergence and rates of weighted sums of associated random variables under the classical assumption of existence of Laplace transforms. This assumption implies the existence of every moment, so we address the same problem assuming a suitable decrease rate on tail joint probabilities which only implies the existence of finitely many moments, proving the analogous characterizations of convergence and rates. Still relaxing further the assumptions on moment existence, we also prove a Marcinkiewicz–Zygmund for associated variables without means, complementing existing results for this dependence structure.