Nonuniform Berry-Esseen bounds for martingales with applications to statistical estimation

Abstract

We establish nonuniform 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 $x\to \infty$. Statistical applications associated with linear regressions and self-normalized large deviations are also provided.

21 pages

References in corpus (2)

• Exponential inequalities for self-normalized martingales with applications
• On the rate of convergence in the martingale central limit theorem