Tests for parallelism and flatness hypotheses of two mean vectors in high-dimensional settings

Abstract

This paper presents test statistics for the hypotheses in profile analysis of high-dimensional data. The existing profile analysis methods on the basis of the Hotelling's $T^2$ suffer from the singularity of the sample covariance matrix when the dimensionality p is larger than the total sample size n. The contribution of this paper is to propose new test statistics for high-dimensional settings with improvements of the approximate percentiles. By simulation results, it can be observed that our proposed test statistics are useful for high-dimensional data under the covariance structure with strong correlations such as the intraclass correlation model. Further, we also observe that our procedures are more powerful than the existing procedure for several cases when $n>p$.

Keywords:

• profile analysis
• high-dimensional data
• asymptotic expansion
• Cauchy–Schwarz inequality
• Monte Carlo simulation

AMS Subject Classification:

• 62H15
• 62E20

Acknowledgements

The authors would like to express their sincere gratitude to the referees who gave invaluable comments and suggestions, which have greatly enhanced this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.