Two-sample Behrens–Fisher problems for high-dimensional data: a normal reference F-type test

Tianming Zhu (), Pengfei Wang () and Jin-Ting Zhang ()
Additional contact information
Tianming Zhu: Nanyang Technological University
Pengfei Wang: Nanyang Technological University
Jin-Ting Zhang: National University of Singapore

Computational Statistics, 2024, vol. 39, issue 6, No 14, 3207-3230

Abstract: Abstract The problem of testing the equality of mean vectors for high-dimensional data has been intensively investigated in the literature. However, most of the existing tests impose strong assumptions on the underlying group covariance matrices which may not be satisfied or hardly be checked in practice. In this article, an F-type test for two-sample Behrens–Fisher problems for high-dimensional data is proposed and studied. When the two samples are normally distributed and when the null hypothesis is valid, the proposed F-type test statistic is shown to be an F-type mixture, a ratio of two independent $$\chi ^2$$ χ 2 -type mixtures. Under some regularity conditions and the null hypothesis, it is shown that the proposed F-type test statistic and the above F-type mixture have the same normal and non-normal limits. It is then justified to approximate the null distribution of the proposed F-type test statistic by that of the F-type mixture, resulting in the so-called normal reference F-type test. Since the F-type mixture is a ratio of two independent $$\chi ^2$$ χ 2 -type mixtures, we employ the Welch–Satterthwaite $$\chi ^2$$ χ 2 -approximation to the distributions of the numerator and the denominator of the F-type mixture respectively, resulting in an approximation F-distribution whose degrees of freedom can be consistently estimated from the data. The asymptotic power of the proposed F-type test is established. Two simulation studies are conducted and they show that in terms of size control, the proposed F-type test outperforms two existing competitors. The good performance of the proposed F-type test is also illustrated by a COVID-19 data example.

Keywords: High-dimensional Behrens–Fisher problem; F-type test; $$\chi ^2$$ χ 2 -type mixtures; F-type mixture; Welch–Satterthwaite $$\chi ^2$$ χ 2 -approximation (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00180-023-01433-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:compst:v:39:y:2024:i:6:d:10.1007_s00180-023-01433-6

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/180/PS2

DOI: 10.1007/s00180-023-01433-6

Access Statistics for this article

Computational Statistics is currently edited by Wataru Sakamoto, Ricardo Cao and Jürgen Symanzik

More articles in Computational Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().