On L
1 Bounds for Asymptotic Normality of Some Weakly Dependent Random Variables |
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Authors: | J Sunklodas |
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Institution: | (1) Institute of Mathematics and Informatics, Akademijos 4, 08663 Vilnius, Lithuania |
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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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Keywords: | ψ -mixing random variables Stein’ s method |
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