Testing high-dimensional mean vector with applications

Jin-Ting Zhang (), Bu Zhou () and Jia Guo ()
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Jin-Ting Zhang: National University of Singapore
Bu Zhou: Zhejiang Gongshang University
Jia Guo: Zhejiang University of Technology

Statistical Papers, 2022, vol. 63, issue 4, No 5, 1105-1137

Abstract: Abstract A centered $$L^2$$ L 2 -norm based test statistic is used for testing if a high-dimensional mean vector equals zero where the data dimension may be much larger than the sample size. Inspired by the fact that under some regularity conditions the asymptotic null distributions of the proposed test are the same as the limiting distributions of a chi-square-mixture, a three-cumulant matched chi-square-approximation is suggested to approximate this null distribution. The asymptotic power of the proposed test under a local alternative is established and the effect of data non-normality is discussed. A simulation study under various settings demonstrates that in terms of size control, the proposed test performs significantly better than some existing competitors. Several real data examples are presented to illustrate the wide applicability of the proposed test to a variety of high-dimensional data analysis problems, including the one-sample problem, paired two-sample problem, and MANOVA for correlated samples or independent samples.

Keywords: High-dimensional data; Matrix variate data; One-sample problem; Two-sample problem; MANOVA; Linear hypothesis; Chi-square-type mixtures; Three-cumulant matched chi-square-approximation (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00362-021-01270-z

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