Non-uniform Berry–Esseen bounds for martingales with applications to statistical estimation. Issue 1 (2nd January 2017) - Fan, X.; Grama, I.; Liu, Q.
ABSTRACT: We establish non-uniform Berry–Esseen bounds for martingales under the conditional Bernstein condition. These bounds imply Cramér type large deviations for moderate x 's, and are of exponential decay rate as de la Peña's inequality whenx → ∞ . Statistical applications associated with linear regressions and self-normalized large deviations are also provided.