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A converse to precise asymptotic results

Let {X,Xn,n[greater-or-equal, slanted]1} be i.i.d. random variables with partial sums {Sn,n[greater-or-equal, slanted]1}, put , and assume there exist functions g and h, such that whenever EX2<[infinity] and EX=0. We prove the converse result, namely that and bn=O(n) imply EX2<[infinity] and EX=0.
Year of publication:
2006
Authors: Li, Deli ; Spataru, Aurel
Published in:
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 76.2006, 5, p. 503-506
Publisher: Elsevier
Keywords: Tail probabilities of sums of i.i.d. random variables Precise asymptotics Symmetrization
Type of publication: Article
Source:
Persistent link: https://www.econbiz.de/10005137941
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