Refined Cramér-type moderate deviation theorems for general self-normalized sums with applications to dependent random variables and winsorized mean
一般自标准化和的精细 Cramér 型中偏差定理及相关变量与缩尾均值应用
Let {(Xi,Yi)}i=1n be a sequence of independent bivariate random vectors. In this paper, we establish a refined Cramér-type moderate deviation theorem for the general self-normalized sum ∑ i=1nXi/(∑i=1nYi2)1/2, which unifies and extends the classical Cramér (Actual. Sci. Ind. 736 (1938) 5–23) theorem and the self-normalized Cramér-type moderate deviation theorems by Jing, Shao and Wang (Ann. Probab. 31 (2003) 2167–2215) as well as the further refined version by Wang (J.…