The Annals of Probability

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

Peter Hall

Full-text: Open access

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

Permanent link to this document
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
links.jstor.org

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

Keywords
Edgeworth expansion moment conditions $t$ statistic

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


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