Geodesic
Further refinement of self-normalized Cramér-type moderate deviations
Sang, Hailin1 ; Ge, Lin2
1 Department of Mathematics, The University of Mississippi, University, MS 38677, Oxford, USA
2 Division of Arts and Sciences, Mississippi State University at Meridian, Meridian, MS 39307, Oxford, USA
ESAIM: Probability and Statistics, Tome 21 (2017), pp. 201-219

Voir la notice de l'article provenant de la source Numdam

In this paper, we study the self-normalized Cramér-type moderate deviations for centered independent random variables X 1 ,X 2 ,... with 0<E|X i | 3 <∞. The main results refine Theorems 1.1 and 1.2 of Wang [Q. Wang, J. Theoret. Probab. 24 (2011) 307–329], the Berry−Esseen bound (2.11) and Corollaries 2.2 and 2.3 of Jing, et al. [B.Y. Jing, Q.M. Shao and Q. Wang, Ann. Probab. 31 (2003) 2167–2215] under stronger moment conditions.

Reçu le :
Accepté le :
DOI : 10.1051/ps/2017010
Classification : 60F10, 62E20
Keywords: Cramér-type moderate deviations, self-normalized sums, normal approximation

Sang, Hailin 1 ; Ge, Lin 2

1 Department of Mathematics, The University of Mississippi, University, MS 38677, Oxford, USA
2 Division of Arts and Sciences, Mississippi State University at Meridian, Meridian, MS 39307, Oxford, USA 
@article{PS_2017__21__201_0,
     author = {Sang, Hailin and Ge, Lin},
     title = {Further refinement of self-normalized {Cram\'er-type} moderate deviations},
     journal = {ESAIM: Probability and Statistics},
     pages = {201--219},
     publisher = {EDP-Sciences},
     volume = {21},
     year = {2017},
     doi = {10.1051/ps/2017010},
     mrnumber = {3716127},
     zbl = {1393.60032},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2017010/}
}
TY  - JOUR
AU  - Sang, Hailin
AU  - Ge, Lin
TI  - Further refinement of self-normalized Cramér-type moderate deviations
JO  - ESAIM: Probability and Statistics
PY  - 2017
SP  - 201
EP  - 219
VL  - 21
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/ps/2017010/
DO  - 10.1051/ps/2017010
LA  - en
ID  - PS_2017__21__201_0
ER  - 
%0 Journal Article
%A Sang, Hailin
%A Ge, Lin
%T Further refinement of self-normalized Cramér-type moderate deviations
%J ESAIM: Probability and Statistics
%D 2017
%P 201-219
%V 21
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ps/2017010/
%R 10.1051/ps/2017010
%G en
%F PS_2017__21__201_0
Sang, Hailin; Ge, Lin. Further refinement of self-normalized Cramér-type moderate deviations. ESAIM: Probability and Statistics, Tome 21 (2017), pp. 201-219. doi: 10.1051/ps/2017010

Cité par Sources :