## Annals of Probability

### Edgeworth Expansion for Student's $t$ Statistic Under Minimal Moment Conditions

Peter Hall

#### Abstract

Recent advances in the theory of Edgeworth expansion allow rigorous estimation of remainder terms, under explicit regularity conditions. However, even in the important case of Student's $t$ statistic, the moment conditions required are unrealistically stringent. In this note we relax those conditions to the minimum needed to define terms in the Edgeworth expansion.

#### Article information

Source
Ann. Probab., Volume 15, Number 3 (1987), 920-931.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176992073

Digital Object Identifier
doi:10.1214/aop/1176992073

Mathematical Reviews number (MathSciNet)
MR893906

Zentralblatt MATH identifier
0626.62019

JSTOR

Subjects
Primary: 60E05: Distributions: general theory
Secondary: 60F05: Central limit and other weak theorems

#### Citation

Hall, Peter. Edgeworth Expansion for Student's $t$ Statistic Under Minimal Moment Conditions. Ann. Probab. 15 (1987), no. 3, 920--931. doi:10.1214/aop/1176992073. https://projecteuclid.org/euclid.aop/1176992073