论文标题
固定序列和应用的自称cramér型中等偏差
Self-normalized Cramér type moderate deviations for stationary sequences and applications
论文作者
论文摘要
令$（x _i）_ {i \ geq1} $为固定序列。表示$ m = \ lfloor n^α\ rfloor，0 <α<1，$和$ k = \ lfloor n/m \ rfloor，$ whene $ \ lfloor a \ rfloor $ stays供$ a。 x_ {m（j-1）+i}，1 \ leq j \ leq k，$ and $ and $（v_k^\ circ）^2 = \ sum_ {j = 1}^k（s_ {j}^\ circ） s_ {j}^\ circ /v_k^\ circ \ geq x）$ as $ n \ to \ infty。
Let $(X _i)_{i\geq1}$ be a stationary sequence. Denote $m=\lfloor n^α\rfloor, 0< α< 1,$ and $ k=\lfloor n/m \rfloor,$ where $\lfloor a \rfloor$ stands for the integer part of $a.$ Set $S_{j}^\circ = \sum_{i=1}^m X_{m(j-1)+i}, 1\leq j \leq k,$ and $ (V_k^\circ)^2 = \sum_{j=1}^k (S_{j}^\circ)^2.$ We prove a Cramér type moderate deviation expansion for $\mathbb{P}( \sum_{j=1}^k S_{j}^\circ /V_k^\circ \geq x)$ as $n\to \infty.$ Applications to mixing type sequences, contracting Markov chains, expanding maps and confidence intervals are discussed.
