On Test Statistics in Profile Analysis with High-dimensional Data

Abstract

We consider profile analysis with unequal covariance matrices under multivariate normality. In particular, we discuss this problem for high-dimensional data where the dimension is larger than the sample size. We propose three test statistics based on Bennett’s (1951) transformation and the Dempster trace criterion proposed by Dempster (1958). We derive the null distributions as well as the nonnull distributions of the test statistics. Finally, in order to investigate the accuracy of the proposed statistics, we perform Monte Carlo simulations for some selected values of parameters.

Keywords:

• Behrens–Fisher problem
• Dempster trace criterion
• High-dimensional data
• Hotelling’s T²-type statistic
• Profile analysis

Mathematics Subject Classification:

• 62H10
• 62H15