A test of sphericity for high-dimensional data and its application for detection of divergently spiked noise. Issue 3 (3rd July 2018)

• Record Type: Journal Article
• Authors: Yata, Kazuyoshi; Aoshima, Makoto; Nakayama, Yugo
• Is Part Of: Sequential analysis. Volume 37:Issue 3(2018)
• Page Start: 397
• Page End: 411
• Publication Date: 2018-07-03
• Subjects: Cross-data-matrix method -- gene expression data -- HDLSS -- noise detection -- noise reduction method -- sphericity; 62H15 -- 62H10 -- 62L10; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2018.1548850
• Languages: English
• ISSNs: 0747-4946

Abstract

Abstract: In this article, we consider a test of the sphericity for high-dimensional covariance matrices. We produce a test statistic by using the extended cross-data-matrix (ECDM) methodology. We show that the ECDM test statistic is based on an unbiased estimator of a sphericity measure. In addition, the ECDM test statistic enjoys consistency properties and the asymptotic normality in high-dimensional settings. We propose a new test procedure based on the ECDM test statistic and evaluate its asymptotic size and power theoretically and numerically. We give a two-stage sampling scheme so that the test procedure can ensure a prespecified level both for the size and power. We apply the test procedure to detect divergently spiked noise in high-dimensional statistical analysis. We analyze gene expression data by the proposed test procedure.