Self-normalized Cramer type moderate deviations for martingales

Xiequan Fan, Ion Grama, Quansheng Liu +1

Let $({\xi }_i,{\mathcal{F}}_i{)}_{i\ge 1}$ be a sequence of martingale differences. Set $S_n={\sum }_{i=1}^n{\xi }_i$ and $[S{]}_n={\sum }_{i=1}^n{\xi }_i^2.$ We prove a Cramér type moderate deviation ex…