Strong moderate deviation theorems are concerned with relative errors in the tails caused by replacing the exact distribution function by its limiting distribution function. A new approach for deriving such theorems is presented using strong approximation inequalities. In this way a strong moderate deviation theorem is obtained for statistics of the form $T(\alpha_n)$, where $T$ is a sublinear functional and $\alpha_n$ is the empirical process. The basic theorem is also applied on linear combinations of order statistics, leading to a substantial improvement of previous results.
Publié le : 1992-04-14
Classification:
Moderate deviations,
Cramer type large deviations,
strong approximation,
sublinear functional,
seminorm,
empirical process,
linear combinations of order statistics,
goodness-of-fit tests,
60F10,
62G30
@article{1176989814,
author = {Inglot, Tadeusz and Kallenberg, Wilbert C. M. and Ledwina, Teresa},
title = {Strong Moderate Deviation Theorems},
journal = {Ann. Probab.},
volume = {20},
number = {4},
year = {1992},
pages = { 987-1003},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989814}
}
Inglot, Tadeusz; Kallenberg, Wilbert C. M.; Ledwina, Teresa. Strong Moderate Deviation Theorems. Ann. Probab., Tome 20 (1992) no. 4, pp. 987-1003. http://gdmltest.u-ga.fr/item/1176989814/