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

Xiequan Fan; Ion Grama; Quansheng Liu

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arXiv · 1608.05217

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

Xiequan Fan·Ion Grama·Quansheng Liu

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Abstract

We establish nonuniform Berry-Esseen bounds for martingales under the conditional Bernstein condition. These bounds imply Cram\'er type large deviations for moderate $x$'s, and are of exponential decay rate as de la Pe\~na's inequality when $x\rightarrow \infty$. Statistical applications associated with linear regressions and self-normalized large deviations are also provided.

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Xiequan Fan, Ion Grama, Quansheng Liu. 2016-08-18. Nonuniform Berry-Esseen bounds for martingales with applications to statistical estimation. https://arxiv.org/abs/1608.05217

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