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A limit result for self-normalized random sums

✍ Scribed by Zhang Li-xin; Wen Ji-wei

Publisher
SP Zhejiang University Press
Year
2001
Tongue
English
Weight
284 KB
Volume
2
Category
Article
ISSN
1009-3095

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We give conditions under which the self-normalized product of independent and identically distributed (i.i.d) random variables X1; X2; : : :, where \* denotes the sum over all n-1-long sequences of integers 16i1Β‘i2Β‘ β€’ β€’ β€’ Β‘in-16n, is asymptotically normally distributed as n β†’ ∞.

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The corresponding moderate deviation principle follows. The Central Limit theorem has been recently obtained by Pang, Lin and Hwang [T.X. Pang, Z.Y. Lin, K.S. Hwang, Asymptotics for self-normalized random products of sums of i.i.d. random variables, J. Math. Anal. Appl. 334 (2007) 1246-1259].