Abstract
In the present paper, we consider L 1 bounds for asymptotic normality for the sequence of r.v.’s X 1,X 2,… (not necessarily stationary) satisfying the ψ-mixing condition. The L 1 bounds have been obtained in terms of Lyapunov fractions which, in a particular case, under finiteness of the third moments of summands and the finiteness of ∑r≥1 r 2 ψ(r), are of order O(n −1/2), where the function ψ participates in the definition of the ψ-mixing condition.
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Sunklodas, J. On L 1 Bounds for Asymptotic Normality of Some Weakly Dependent Random Variables. Acta Appl Math 102, 87–98 (2008). https://doi.org/10.1007/s10440-008-9211-9
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DOI: https://doi.org/10.1007/s10440-008-9211-9