Mean test for high-dimensional data based on covariance matrix with linear structures

Guanpeng Wang (), Yuyuan Wang () and Hengjian Cui ()
Additional contact information
Guanpeng Wang: Weifang University
Yuyuan Wang: Hong Kong Baptist University
Hengjian Cui: Capital Normal University

Metrika: International Journal for Theoretical and Applied Statistics, 2025, vol. 88, issue 5, No 3, 657-678

Abstract: Abstract In this work, the mean test is considered under the condition that the number of dimensions p is much larger than the sample size n when the covariance matrix is represented as a linear structure as possible. At first, the estimator of coefficients in the linear structures of the covariance matrix is constructed, and then an efficient covariance matrix estimator is naturally given. Next, a new test statistic similar to the classical Hotelling’s $$T^2$$ T 2 test is proposed by replacing the sample covariance matrix with the given estimator of covariance matrix. Then the asymptotic normality of the estimator of coefficients and that of a new statistic for the mean test are separately obtained under some mild conditions. Simulation results show that the performance of the proposed test statistic is almost the same as the Hotelling’s $$T^2$$ T 2 test statistic for which the covariance matrix is known. Our new test statistic can not only control reasonably the nominal level; it also gains greater empirical powers than competing tests. It is found that the power of mean test has great improvement when considering the structure information of the covariance matrix, especially for high-dimensional cases. Moreover, an example with real data is provided to show the application of our approach.

Keywords: Asymptotic normality; Covariance matrix structure; High dimension; Mean test (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00184-024-00971-3 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:metrik:v:88:y:2025:i:5:d:10.1007_s00184-024-00971-3

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/184/PS2

DOI: 10.1007/s00184-024-00971-3

Access Statistics for this article

Metrika: International Journal for Theoretical and Applied Statistics is currently edited by U. Kamps and Norbert Henze

More articles in Metrika: International Journal for Theoretical and Applied Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().