Further refinement of self-normalized Cramér-type moderate deviations

Sang, Hailin; Ge, Lin

doi:10.1051/ps/2017010

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

ESAIM: Probability and Statistics, Tome 21 (2017), pp. 201-219.

Résumé

In this paper, we study the self-normalized Cramér-type moderate deviations for centered independent random variables $X_{1}, X_{2}, . . .$ with $0 < E | X_{i} |^{3} < \infty$ . 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 : 2015-01-29
Accepté le : 2017-05-12

MR Zbl

DOI : 10.1051/ps/2017010

Classification : 60F10, 62E20
Mots-clés : Cramér-type moderate deviations, self-normalized sums, normal approximation

Affiliations des auteurs :

Sang, Hailin ¹ ; Ge, Lin ²

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     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://www.numdam.org/articles/10.1051/ps/2017010/}
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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. http://www.numdam.org/articles/10.1051/ps/2017010/

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