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

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 
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     title = {Further refinement of self-normalized {Cram\'er-type} moderate deviations},
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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

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