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Cram\'{e}r type moderate deviations for self-normalized $\psi$-mixing sequences. (arXiv:1810.01099v1 [math.PR])
来源于:arXiv
Let $(\eta_i)_{i\geq1}$ be a sequence of $\psi$-mixing random variables. Let
$m=\lfloor n^\alpha \rfloor, 0< \alpha < 1, k=\lfloor n/m \rfloor,$ and $Y_j =
\sum_{i=1}^m \eta_{m(j-1)+i}, 1\leq j \leq k.$ 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 $n\to
\infty.$ Our result is similar to the recent work of Chen et al.\,\cite{CSWX16}
where the authors established Cram\'er type moderate deviation expansions for
$\beta$-mixing sequences. Comparing to the result of Chen et al.\, (2016), our
results hold for mixing coefficients with polynomial decaying rate and wider
ranges of validity. 查看全文>>