### 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 |
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Pages (from-to) | 987-1003 |

Number of pages | 17 |

Journal | Annals of probability |

Volume | 20 |

Issue number | 2 |

DOIs | |

Publication status | 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

## Cite this

Inglot, T., Kallenberg, W. C. M., & Ledwina, T. (1992). Strong moderate deviation theorems.

*Annals of probability*,*20*(2), 987-1003. https://doi.org/10.1214/aop/1176989814