Open Access
April, 1992 Strong Moderate Deviation Theorems
Tadeusz Inglot, Wilbert C. M. Kallenberg, Teresa Ledwina
Ann. Probab. 20(2): 987-1003 (April, 1992). DOI: 10.1214/aop/1176989814


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.


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Tadeusz Inglot. Wilbert C. M. Kallenberg. Teresa Ledwina. "Strong Moderate Deviation Theorems." Ann. Probab. 20 (2) 987 - 1003, April, 1992.


Published: April, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0757.60015
MathSciNet: MR1159582
Digital Object Identifier: 10.1214/aop/1176989814

Primary: 60F10
Secondary: 62G30

Keywords: Cramer type large deviations , empirical process , Goodness-of-fit tests , linear combinations of order statistics , Moderate deviations , seminorm , strong approximation , sublinear functional

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 2 • April, 1992
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