Further Refinement of Self-normalized Cram\a'{e}r-type moderate Deviations

Hailin Sang; Lin Ge

Further Refinement of Self-normalized Cram\a'{e}r-type moderate Deviations

Probability 2017-05-19 v4

Authors: Hailin Sang , Lin Ge

Abstract

In this paper, we study the self-normalized Cram\a'{e}r-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 (2011), the Berry-Esseen bound (2.11) and Corollaries 2.2 and 2.3 of Jing, Shao and Wang (2003) under stronger moment conditions.

Keywords

probability theory

Cite

@article{arxiv.1309.5433,
  title  = {Further Refinement of Self-normalized Cram\a'{e}r-type moderate Deviations},
  author = {Hailin Sang and Lin Ge},
  journal= {arXiv preprint arXiv:1309.5433},
  year   = {2017}
}

Comments

20 pages, accepted by ESAIM: P&S

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