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Moderate Deviations for I.I.D. Random Variables

Published online by Cambridge University Press:  15 May 2003

Peter Eichelsbacher  and
Matthias Löwe
Peter Eichelsbacher
Affiliation:
Ruhr-Universität Bochum, Fakultät für Mathematik, NA3/68, 44780 Bochum, Germany; peter.eichelsbacher@ruhr-uni-bochum.de.
Matthias Löwe
Affiliation:
Department of Mathematics, University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands; loewe@sci.kun.nl.
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Abstract

We derive necessary and sufficient conditions for a sum of i.i.d. random variables $\sum_{i=1}^n X_i/b_n$ – where $\frac {b_n} n \downarrow 0$, but $\frac {b_n} {\sqrt n} \uparrow \infty$ – to satisfy a moderate deviations principle. Moreover we show that this equivalence is a typical moderate deviations phenomenon. It is not true in a large deviations regime.

Keywords

Moderate deviationslarge deviations.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 7 , March 2003 , pp. 209 - 218
Copyright
© EDP Sciences, SMAI, 2003

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