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

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.

20 pages, accepted by ESAIM: P&S

References in corpus (1)

• Saddlepoint approximation for Student's t-statistic with no moment conditions