RETRACTED ARTICLE: Convergence of Weighted Sums for Arrays of Negatively Dependent Random Variables and Its Applications

Jong-Il Baek () and Sung-Tae Park ()
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Jong-Il Baek: Wonkwang University
Sung-Tae Park: Wonkwang University

Journal of Theoretical Probability, 2010, vol. 23, issue 2, 362-377

Abstract: Abstract We discuss the complete convergence of weighted sums for arrays of rowwise negatively dependent random variables (ND r.v.’s) to linear processes. As an application, we obtain the complete convergence of linear processes based on ND r.v.’s which extends the result of Li et al. (Stat. Probab. Lett. 14:111–114, 1992), including the results of Baum and Katz (Trans. Am. Math. Soc. 120:108–123, 1965), from the i.i.d. case to a negatively dependent (ND) setting. We complement the results of Ahmed et al. (Stat. Probab. Lett. 58:185–194, 2002) and confirm their conjecture on linear processes in the ND case.

Keywords: Complete convergence; Negatively dependent random variables; Linear processes; 60G50; 60F15 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10959-008-0198-y

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