Almost Sure Central Limit Theorems for Heavily Trimmed Sums
β Scribed by Fang Wang; Shi Hong Cheng
- Publisher
- Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2004
- Tongue
- English
- Weight
- 186 KB
- Volume
- 20
- Category
- Article
- ISSN
- 1439-7617
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract Let __X__, __X__~1~, __X__~2~, β¦ be i.i.d. random variables with nondegenerate common distribution function __F__, satisfying __EX__ = 0, __EX__^2^ = 1. Let __X~i~__ and __M~n~__ = max{__X~i~__, 1 β€ __i__ β€ __n__ }. Suppose there exists constants __a~n~__ > 0, __b~n~__ β __R__ and a non
## Abstract A general almost sure limit theorem is presented for random fields. It is applied to obtain almost sure versions of some (functional) central limit theorems. (Β© 2003 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
## Abstract Let {__S~n~__, __n__ β₯ 1} be partial sums of independent identically distributed random variables. The almost sure version of CLT is generalized on the case of randomly indexed sums {__S~Nn~__, __n__ β₯ 1}, where {__N~n~__, __n__ β₯ 1} is a sequence of positive integerβvalued random varia