Tests for the parallelism and flatness hypotheses of multi-group profile analysis for high-dimensional elliptical populations

This paper is concerned with tests for the parallelism and flatness hypotheses in multi-group profile analysis for high-dimensional data. We extend to elliptical distributions the procedures developed for normal populations by Harrar and Kong (2016). Specifically, we prove that their statistics continue to be asymptotically normal when the underlying population is elliptical, and we obtain new tests by improving their estimator of the asymptotic variance. Using asymptotic normality, we show that the asymptotic size of the proposed tests is equal to the nominal significance level, and we also derive the asymptotic power. Finally, we present simulation results and find that the power of the new tests is superior to that of the original Harrar-Kong procedure.