A Limit Theorem for the Moment of Self-Normalized Sums. (14th July 2009)

• Record Type: Journal Article
• Authors: Zang, Qing-pei
• Other Names: Dshalalow Jewgeni Academic Editor.
• Is Part Of: Journal of inequalities and applications. Volume 2009(2009)
• Publication Date: 2009-07-14
• Subjects: Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/2009/957056
• Languages: English
• ISSNs: 1029-242X

Abstract

Abstract : Let{ X, X n ; n ≥ 1 } be a sequence of independent and identically distributed ( i.i.d. ) random variables andX is in the domain of attraction of the normal law andE X = 0 . For1 ≤ p < 2, b > − 1, we prove the precise asymptotics in Davis law of large numbers for∑ n = 1 ∞ ( ( log n ) b / n ) E { ( | S n | / V n ) − ε ( 2 log n ) ( 2 − p ) / ( 2 p ) } + as ε ↘ 0.