Moderate Deviations for I.I.D. Random Variables

Peter Eichelsbacher; Matthias Löwe

ESAIM: Probability and Statistics (2010)

  • Volume: 7, page 209-218
  • ISSN: 1292-8100

Abstract

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We derive necessary and sufficient conditions for a sum of i.i.d. random variables ∑ i = 1 n X i / b n – where b n n ↓ 0 , but b n n ↑ ∞ – 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.

How to cite

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Eichelsbacher, Peter, and Löwe, Matthias. "Moderate Deviations for I.I.D. Random Variables." ESAIM: Probability and Statistics 7 (2010): 209-218. <http://eudml.org/doc/104304>.

@article{Eichelsbacher2010,
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. },
author = {Eichelsbacher, Peter, Löwe, Matthias},
journal = {ESAIM: Probability and Statistics},
keywords = {Moderate deviations; large deviations.; moderate deviations; large deviations},
language = {eng},
month = {3},
pages = {209-218},
publisher = {EDP Sciences},
title = {Moderate Deviations for I.I.D. Random Variables},
url = {http://eudml.org/doc/104304},
volume = {7},
year = {2010},
}

TY - JOUR
AU - Eichelsbacher, Peter
AU - Löwe, Matthias
TI - Moderate Deviations for I.I.D. Random Variables
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 7
SP - 209
EP - 218
AB - 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.
LA - eng
KW - Moderate deviations; large deviations.; moderate deviations; large deviations
UR - http://eudml.org/doc/104304
ER -

References

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  7. P. Eichelsbacher and U. Schmock, Rank-dependent moderate deviations for U-empirical measures in strong topologies(submitted).  
  8. E. Giné and V. de la Pe na, Decoupling: From dependence to independence. Springer-Verlag (1999).  
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