Non-uniform Berry–Esseen bounds formartingales with applications to statistical estimation
Résumé
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 when x tends to infinity. Statistical applications associated with linear regressions and self-normalized large deviations are also provided.