Geodesic
Moderate deviations for I.I.D. random variables
ESAIM: Probability and Statistics, Tome 7 (2003), pp. 209-218

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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.

DOI : 10.1051/ps:2003005
Classification : 60F10
Keywords: moderate deviations, large deviations 
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     author = {Eichelsbacher, Peter and L\"owe, Matthias},
     title = {Moderate deviations for {I.I.D.} random variables},
     journal = {ESAIM: Probability and Statistics},
     pages = {209--218},
     publisher = {EDP-Sciences},
     volume = {7},
     year = {2003},
     doi = {10.1051/ps:2003005},
     mrnumber = {1956079},
     zbl = {1019.60021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2003005/}
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Eichelsbacher, Peter; Löwe, Matthias. Moderate deviations for I.I.D. random variables. ESAIM: Probability and Statistics, Tome 7 (2003), pp. 209-218. doi: 10.1051/ps:2003005

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