Two-sample Behrens-Fisher problems for high-dimensional data: a normal reference scale-invariant test.

Content Provider	Europe PMC
Author	Zhang, Liang Zhu, Tianming Zhang, Jin-Ting
Copyright Year	2020
Abstract	ABSTRACT For high-dimensional two-sample Behrens–Fisher problems, several non-scale-invariant and scale-invariant tests have been proposed. Most of them impose strong assumptions on the underlying group covariance matrices so that their test statistics are asymptotically normal. However, in practice, these assumptions may not be satisfied or hardly be checked so that these tests may not be able to maintain the nominal size well in practice. To overcome this difficulty, in this paper, a normal reference scale-invariant test is proposed and studied. It works well by neither imposing strong assumptions on the underlying group covariance matrices nor assuming their equality. It is shown that under some regularity conditions and the null hypothesis, the proposed test and a chi-square-type mixture have the same normal and non-normal limiting distributions. It is then justifiable to approximate the null distribution of the proposed test using that of the chi-square-type mixture. The distribution of the chi-square type mixture can be well approximated by the Welch–Satterthwaite chi-square-approximation with the approximation parameter consistently estimated from the data. The asymptotic power of the proposed test is established. Numerical results demonstrate that the proposed test has much better size control and power than several well-known non-scale-invariant and scale-invariant tests.
Related Links	https://europepmc.org/backend/ptpmcrender.fcgi?accid=PMC9930866&blobtype=pdf
Page Count	21
ISSN	02664763
Volume Number	50
DOI	10.1080/02664763.2020.1834516
PubMed Central reference number	PMC9930866
Issue Number	3
PubMed reference number	36819075
Journal	Journal of Applied Statistics [J Appl Stat]
e-ISSN	13600532
Language	English
Publisher	Taylor & Francis
Publisher Date	2020-10-19
Access Restriction	Open
Rights License	© 2020 Informa UK Limited, trading as Taylor & Francis Group
Subject Keyword	High-dimensional data scale-invariant test χ2-type mixture two-sample test Welch–Satterthwaite χ2-approximation Behrens–Fisher problem
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty