On almost sure convergence for weighted sums of pairwise negatively quadrant dependent random variables

H. Jabbari ()

Statistical Papers, 2013, vol. 54, issue 3, 765-772

Abstract: Let {X n , n ≥ 1} be a sequence of pairwise negatively quadrant dependent (NQD) random variables. In this study, we prove almost sure limit theorems for weighted sums of the random variables. From these results, we obtain a version of the Glivenko–Cantelli lemma for pairwise NQD random variables under some fragile conditions. Moreover, a simulation study is done to compare the convergence rates with those of Azarnoosh (Pak J Statist 19(1):15–23, 2003 ) and Li et al. (Bull Inst Math 1:281–305, 2006 ). Copyright Springer-Verlag 2013

Keywords: Almost sure limit theorem; Glivenko–Cantelli lemma; Negatively quadrant dependent; Weighted sums; 60F15; 62G20 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s00362-012-0460-3

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