Geodesic
A~Gibbs conditional theorem under extreme deviation
Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 3, pp. 489-518

Voir la notice de l'article provenant de la source Math-Net.Ru

We explore some properties of the conditional distribution of an independently and identically distributed (i.i.d.) sample under large exceedances of its sum. Thresholds for the asymptotic independence of the summands are observed, in contrast with the classical case when the conditioning event is in the range of a large deviation. This paper is an extension of Broniatowski and Cao [Extremes, 17 (2014), pp. 305–336]. Tools include a new Edgeworth expansion adapted to specific triangular arrays, where the rows are generated by tilted distribution with diverging parameters, and some Abelian type results.
Keywords: Gibbs conditional principle, extreme deviation. 
@article{TVP_2022_67_3_a4,
     author = {M. Biret and M. Broniatowski and Z. Cao},
     title = {A~Gibbs conditional theorem under extreme deviation},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {489--518},
     publisher = {mathdoc},
     volume = {67},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2022_67_3_a4/}
}
TY  - JOUR
AU  - M. Biret
AU  - M. Broniatowski
AU  - Z. Cao
TI  - A~Gibbs conditional theorem under extreme deviation
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2022
SP  - 489
EP  - 518
VL  - 67
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_2022_67_3_a4/
LA  - ru
ID  - TVP_2022_67_3_a4
ER  - 
%0 Journal Article
%A M. Biret
%A M. Broniatowski
%A Z. Cao
%T A~Gibbs conditional theorem under extreme deviation
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2022
%P 489-518
%V 67
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_2022_67_3_a4/
%G ru
%F TVP_2022_67_3_a4
M. Biret; M. Broniatowski; Z. Cao. A~Gibbs conditional theorem under extreme deviation. Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 3, pp. 489-518. http://geodesic.mathdoc.fr/item/TVP_2022_67_3_a4/