Self-normalized central limit theorem and estimation of variance of partial sums for negative dependent random variables
β Scribed by Lixin Zhang; Strongway Shi
- Book ID
- 107500526
- Publisher
- SP Editorial Committee of Applied Mathematics - A Journal of Chinese Universities
- Year
- 2002
- Tongue
- English
- Weight
- 325 KB
- Volume
- 17
- Category
- Article
- ISSN
- 1005-1031
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π SIMILAR VOLUMES
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 β.
In this paper, we establish a new limit theorem for partial sums of random variables. As corollaries, we generalize the extended Borel-Cantelli lemma, and obtain some strong laws of large numbers for Markov chains as well as a generalized strong ergodic theorem for irreducible and positive recurrent