Darling--Erdős theorem for self-normalized sums
Date
2003
Authors
Csörgő, Miklós
Szyszkowicz, Barbara
Wang, Qiying
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Publisher
Institute of Mathematical Statistics
Abstract
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.
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Keywords
Darling–Erdos theorem, Erdos–Feller–Kolmogorov–Petrovski test, self- normalized sums
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Source
The Annals of Probability
Type
Journal article
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Open Access
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