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
Access Full Article
top
Abstract
topHow to cite
topEichelsbacher, 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
top- A. de Acosta, Moderate deviations and associated Laplace approximations for sums of independent random vectors. Trans. Amer. Math. Soc.329 (1992) 357-375.
- M.A. Arcones, The large deviation principle for empirical processes. Preprint (1999).
- M. van den Berg, E. Bolthausen and F. den Hollander, Moderate deviations for the volume of the Wiener sausage. Ann. Math.153 (2001) 355-406.
- H. Cramér, Sur un nouveau théorème-limite de la théorie des probabilités, Actualités Scientifique et Industrielles (736 Colloque consacré à la théorie des probabilités). Hermann (1938) 5-23.
- A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications. Springer, New York (1998).
- M. Djellout, Moderate deviations for martingale differences and applications to Φ-mixing sequences. Stochastics and Stochastic Reports (to appear).
- P. Eichelsbacher and U. Schmock, Rank-dependent moderate deviations for U-empirical measures in strong topologies(submitted).
- E. Giné and V. de la Pe na, Decoupling: From dependence to independence. Springer-Verlag (1999).
- M. Ledoux, Sur les déviations modérées des sommes de variables aléatoires vectorielles indépendantes de même loi. Ann. Inst. H. Poincaré28 (1992) 267-280.
- M. Ledoux and M. Talagrand, Probability in Banach Spaces. Springer-Verlag, Berlin (1991).
- M. Löwe and F. Merkl, Moderate deviations for longest increasing subsequences: The upper tail. Comm. Pure Appl. Math.54 (2001) 1488-1520.
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.