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Cramer Type Moderate deviations for the Maximum of Self-normalized Sums

Authors Hu, Zhishui
Shao, Qi-Man View this author's profile
Wang, Qiying
Issue Date 2009
Source Electronic journal of probability , v. 14, 2009, MAY 31, p. 1181-1197
Summary Let {X, X-i, i >= 1} be i.i.d. random variables, S-k be the partial sum and V-n(2) = Sigma(n)(i=1) X-i(2). Assume that E(X) = 0 and E(X-4) < infinity. In this paper we discuss the moderate deviations of the maximum of the self-normalized sums. In particular, we prove that P(max(1 <= k <= n) S-k >= x V-n)/(1 - Phi(x)) --> 2 uniformly in x is an element of [0, o(n(1/6))).
ISSN 1083-6489
Language English
Format Article
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