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Darling--Erdős theorem for self-normalized sums

Csörgő, Miklós; Szyszkowicz, Barbara; Wang, Qiying


Let X, X1, X2,... be i.i.d. nondegenerate random variables, Sn = ∑j=1n Xj and Vn2 = ∑j=1n. We investigate the asymptotic behavior in distribution of the maximum of self-normalized sums, max1≤k≤n Sk/Vk, and the law of the iterated logarithm for self-normalized sums, Sn/Vn, 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.

CollectionsANU Research Publications
Date published: 2003
Type: Journal article
Source: The Annals of Probability
DOI: 10.1214/aop/1048516532
Access Rights: Open Access


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