Darling-Erdos theorem for self-normalized sums

• 成果类型: Article
• 署名作者: Csörgo, M; Szyszkowicz, B; Wang, QY
• 署名单位: Carleton University; Australian National University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2003
• 页码: 676-692
• 关键词: random-variables

摘要

Let X, X-1, X-2,... be i.i.d. nondegenerate random variables, S-n = Sigma(j=1)(n) X-j and V-n(2) = Sigma(j=1)(n) X-j(2). We investigate the asymptotic behavior in distribution of the maximum of self-normalized sums, max(1less than or equal tokless than or equal ton) S-k/V-k, and the law of the iterated logarithm for self-normalized sums, S-n/V-n, when X belongs to the domain of attraction of the normal law. In this context, we establish a Darling-Erdos-type theorem as well as an Erdos-Feller-Kolmogorov-Petrovski-type test for self-normalized sums.