Abstract
A complete convergence result is obtained for weighted sums of identically distributed ρ *-mixing random variables with E|X 1|α log(1 + |X 1|) < ∞ for some 0 < α ≤ 2. This result partially extends the result of Sung (Stat Papers 52: 447–454, 2011) for negatively associated random variables to ρ *-mixing random variables. It also settles the open problem posed by Zhou et al. (J Inequal Appl, 2011, doi:10.1155/2011/157816).
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Sung, S.H. On the strong convergence for weighted sums of ρ *-mixing random variables. Stat Papers 54, 773–781 (2013). https://doi.org/10.1007/s00362-012-0461-2
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DOI: https://doi.org/10.1007/s00362-012-0461-2