Sharp Cramér-type moderate deviation bounds for the self-normalized maximum of partial sums

Song-Hao Liu, Qi-Man Shao, Hao Shi +1

Let $X_1,X_2,\dots$ be i.i.d. random variables with zero mean and variance ${\sigma }^2\in (0,\infty )$. In this paper, we establish a sharp Cramér-type moderate deviation for the self-norm…