A Behrens–Fisher problem for general factor models in high dimensions

Masashi Hyodo, Takahiro Nishiyama and Tatjana Pavlenko

Journal of Multivariate Analysis, 2023, vol. 195, issue C

Abstract: We revisit the well-known Behrens–Fisher problem in an original and challenging high-dimensional framework, and propose a testing procedure which accommodates a low-dimensional latent factor model. The developed inferential framework is general, as it applies to problems where the underlying populations may be non-normal, the dimension of the population mean vectors may highly exceed the sample size, the design may be unbalanced, and the loading factor dimensions may be different. Under a high-dimensional asymptotic regime, combined with fairly weak technical conditions, we show that null limiting distributions of the test statistics follow a weighted mixture of chi-square distributions, which depends only on the spectrum of the noise covariance matrix and the number of latent factors. As these latter are usually unknown in practice, we exploit an estimation procedure which builds on recent advances in random matrix theory. The asymptotic power of the proposed test is established. A numerical study confirms good analytical properties of the new test that compares favorably to existing procedures used in a similar context. Real data applications are demonstrated with a study of a leukemia data set.

Keywords: High-dimensional data; High-dimensional testing problem; Latent factor model; Two-sample test (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X23000088
Full text for ScienceDirect subscribers only

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:eee:jmvana:v:195:y:2023:i:c:s0047259x23000088

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2023.105162

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().