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Nonuniform Berry-Esseen bounds for martingales with applications to statistical estimation
- Source :
- Statistics, 2017, 51(1): 105-122
- Publication Year :
- 2016
-
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.<br />Comment: 21 pages
- Subjects :
- Mathematics - Probability
60G42, 60F05, 60F10, 60E15, 62E20, 62J05
Subjects
Details
- Database :
- arXiv
- Journal :
- Statistics, 2017, 51(1): 105-122
- Publication Type :
- Report
- Accession number :
- edsarx.1608.05217
- Document Type :
- Working Paper