Volume 21, 2017
|Page(s)||201 - 219|
|Published online||19 October 2017|
Further refinement of self-normalized Cramér-type moderate deviations∗
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
Received: 29 January 2015
Revised: 6 September 2016
Accepted: 12 May 2017
In this paper, we study the self-normalized Cramér-type moderate deviations for centered independent random variables X1,X2,... with 0 <E | Xi | 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.
Mathematics Subject Classification: 60F10 / 62E20
Key words: Cramér-type moderate deviations / self-normalized sums / normal approximation
© EDP Sciences, SMAI, 2017
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