Deviation inequalities for martingales with applications to linear regressions and weak invariance principles
Probability
2017-08-03 v1
Abstract
Using changes of probability measure developed by \mbox{Grama} and Haeusler (Stochastic Process.\ Appl., 2000), we obtain two generalizations of the deviation inequalities of Lanzinger and Stadtm\"{u}ller (Stochastic Process.\ Appl., 2000) and Fuk and Nagaev (Theory Probab. Appl., 1971) to the case of martingales. Our inequalities recover the best possible decaying rate of independent case. Applications to linear regressions and weak invariance principles for martingales are provided.
Keywords
Cite
@article{arxiv.1504.03667,
title = {Deviation inequalities for martingales with applications to linear regressions and weak invariance principles},
author = {Xiequan Fan},
journal= {arXiv preprint arXiv:1504.03667},
year = {2017}
}