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- W3099872972 abstract "Let $X_1,X_2,...$ be independent random variables with zero means and finite variances, and let $S_n=sum_{i=1}^nX_i$ and $V^2_n=sum_{i=1}^nX^2_i$. A Cram'{e}r type moderate deviation for the maximum of the self-normalized sums $max_{1leq kleq n}S_k/V_n$ is obtained. In particular, for identically distributed $X_1,X_2,...,$ it is proved that $P(max_{1leq kleq n}S_kgeq xV_n)/(1-Phi (x))rightarrow2$ uniformly for $0<xleqmathrm{o}(n^{1/6})$ under the optimal finite third moment of $X_1$." @default.
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- W3099872972 date "2013-08-01" @default.
- W3099872972 modified "2023-10-02" @default.
- W3099872972 title "Self-normalized Cramér type moderate deviations for the maximum of sums" @default.
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- W3099872972 doi "https://doi.org/10.3150/12-bej415" @default.
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