Wu, Yongfeng; Wang, Dingcheng Convergence properties for arrays of rowwise pairwise negatively quadrant dependent random variables. (English) Zbl 1265.60067 Appl. Math., Praha 57, No. 5, 463-475 (2012). The paper presents convergence properties for arrays of rowwise pairwise negatively quadrant dependent random variables. Particularly complete convergence and convergence in \(L_{p}\) are investigated. The results extend and improve corresponding results of T. C. Hu and R. L. Taylor [Int. J. Math. Math. Sci. 20, No. 2, 375–382 (1997; Zbl 0883.60024)]. Reviewer: Petr Lachout (Praha) Cited in 5 Documents MSC: 60F15 Strong limit theorems 60F25 \(L^p\)-limit theorems Keywords:complete convergence; complete moment convergence; \(L_p\) convergence; pairwise NQD random variables Citations:Zbl 0883.60024 PDF BibTeX XML Cite \textit{Y. Wu} and \textit{D. Wang}, Appl. Math., Praha 57, No. 5, 463--475 (2012; Zbl 1265.60067) Full Text: DOI Link References: [1] A. Adler, A. Rosalsky, A. Volodin: A mean convergence theorem and weak law for arrays of random elements in martingale type p Banach spaces. Stat. Probab. Lett. 32 (1997), 167–174. · Zbl 0874.60008 [2] W. Bryc, W. Smoleński: Moment conditions for almost sure convergence of weakly correlated random variables. Proc. Am. Math. Soc. 119 (1993), 629–635. · Zbl 0785.60018 [3] Y. S. Chow: On the rate of moment complete convergence of sample sums and extremes. Bull. Inst. Math. Acad. Sin. 16 (1988), 177–201. · Zbl 0655.60028 [4] N. Ebrahimi, M. Ghosh: Multivariate negative dependence. Commun. Stat., Theory Methods 10 (1981), 307–337. · Zbl 0506.62034 [5] S.X. Gan, P.Y. Chen: On the limiting behavior of the maximum partial sums for arrays of rowwise NA random variables. Acta Math. Sci., Ser. B, Engl. Ed. 27 (2007), 283–290. · Zbl 1125.60027 [6] P. L. Hsu, H. Robbins: Complete convergence and the law of large numbers. Proc. Natl. Acad. Sci. 33 (1947), 25–31. · Zbl 0030.20101 [7] T.C. Hu, R. L. Taylor: On the strong law for arrays and for the bootstrap mean and variance. Int. J. Math. Math. Sci. 20 (1997), 375–382. · Zbl 0883.60024 [8] K. Joag-Dev, F. Proschan: Negative association of random variables with applications. Ann. Stat. 11 (1983), 286–295. · Zbl 0508.62041 [9] E. L. Lehmann: Some concepts of dependence. Ann. Math. Stat. 37 (1966), 1137–1153. · Zbl 0146.40601 [10] D.C. Wang, W. Zhao: Moment complete convergence for sums of a sequence of NA random variables. Appl. Math., Ser. A (Chin. Ed.) 21 (2006), 445–450. (In Chinese.) · Zbl 1137.60320 [11] Q.Y. Wu: Convergence properties of pairwise NQD random sequences. Acta Math. Sin. 45 (2002), 617–624. (In Chinese.) · Zbl 1008.60039 [12] Y.F. Wu, D. J. Zhu: Convergence properties of partial sums for arrays of rowwise negatively orthant dependent random variables. J. Korean Stat. Soc. 39 (2010), 189–197. · Zbl 1294.60056 [13] S.C. Yang: Almost sure convergence of weighted sums of mixing sequences. J. Syst. Sci. Math. Sci. 15 (1995), 254–265. (In Chinese.) · Zbl 0869.60029 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.