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- W2894744608 abstract "Let $(eta_i)_{igeq1}$ be a sequence of $psi$-mixing random variables. Let $m=lfloor n^alpha rfloor, 0< alpha < 1, k=lfloor n/(2m) rfloor,$ and $Y_j = sum_{i=1}^m eta_{m(j-1)+i}, 1leq j leq k.$ Set $ S_k^o=sum_{j=1}^{k } Y_j $ and $[S^o]_k=sum_{i=1}^{k } (Y_j )^2.$ We prove a Cram'er type moderate deviation expansion for $mathbb{P}(S_k^o/sqrt{[ S^o]_k} geq x)$ as $nto infty.$ Our result is similar to the recent work of Chentextit{ et al.} [Self-normalized Cram'{e}r-type moderate deviations under dependence. Ann. Statist. 2016; textbf{44}(4): 1593--1617] where the authors established Cram'er type moderate deviation expansions for $beta$-mixing sequences. Comparing to the result of Chen textit{et al.}, our results hold for mixing coefficients with polynomial decaying rate and wider ranges of validity." @default.
- W2894744608 created "2018-10-12" @default.
- W2894744608 creator A5026371023 @default.
- W2894744608 date "2018-10-02" @default.
- W2894744608 modified "2023-09-27" @default.
- W2894744608 title "Cram'{e}r type moderate deviations for self-normalized $psi$-mixing sequences" @default.
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- W2894744608 doi "https://doi.org/10.48550/arxiv.1810.01099" @default.
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