Please use this identifier to cite or link to this item:
Title: Limiting distributions of the non-central t-statistic and their applications to the power of t-tests under non-normality
Authors: Bentkus, V.
Jing, B.-Y.
Shao, Q.-M.
Zhou, W. 
Keywords: Domain of attraction
Limit theorems
Non-central t-statistic
Power of t-test
Issue Date: 2007
Citation: Bentkus, V., Jing, B.-Y., Shao, Q.-M., Zhou, W. (2007). Limiting distributions of the non-central t-statistic and their applications to the power of t-tests under non-normality. Bernoulli 13 (2) : 346-364. ScholarBank@NUS Repository.
Abstract: Let X1, X2,... be a sequence of independent and identically distributed random variables. Let X be an independent copy of X1. Define Tn = √nX/S, where X and S2 are the sample mean and the sample variance, respectively. We refer to Tn as the central or non-central (Student's) t-statistic, depending on whether EX = 0 or EX ≠ 0, respectively. The non-central t-statistic arises naturally in the calculation of powers for t-tests. The central t-statistic has been well studied, while there is a very limited literature on the non-central t-statistic. In this paper, we attempt to narrow this gap by studying the limiting behaviour of the non-central t-statistic, which turns out to be quite complicated. For instance, it is well known that, under finite second-moment conditions, the limiting distributions for the central t-statistic are normal while those for the non-central t-statistic can be non-normal and can critically depend on whether or not EX4 = ∞. As an application, we study the effect of non-normality on the performance of the t-test. © 2007 ISI/BS.
Source Title: Bernoulli
ISSN: 13507265
DOI: 10.3150/07-BEJ5073
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.


checked on Mar 25, 2019


checked on Mar 25, 2019

Page view(s)

checked on Mar 1, 2019

Google ScholarTM



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.