In this note, we discuss the Kolmogrov and Erd os test for self-normalized sums. Some general results are obtained.
Estimation of distribution tails for normalized and self-normalized sums
β Scribed by V. A. Egorov
- Publisher
- Springer US
- Year
- 2005
- Tongue
- English
- Weight
- 122 KB
- Volume
- 127
- Category
- Article
- ISSN
- 1573-8795
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π SIMILAR VOLUMES
a b s t r a c t Let {X, X n ; n β₯ 1} be a sequence of independent and identically distributed (i.i.d.) random variables with X in the domain of attraction of the normal law and EX = 0. In this note, we obtain a new kind of complete moment convergence for self-normalized sums.
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].