# Strong moderate deviation theorems

Tadeusz Inglot, W.C.M. Kallenberg, Teresa Ledwina

## Abstract

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.
Original language Undefined 987-1003 17 Annals of probability 20 2 https://doi.org/10.1214/aop/1176989814 Published - 1992

## Keywords

• Cramer type large deviations
• empirical process
• strong approximation
• sublinear functional
• METIS-140514
• linear combinations of order statistics
• seminorm
• Moderate deviations
• IR-70374
• goodness-of-fit tests