Linear hypothesis testing in high-dimensional heteroscedastic one-way MANOVA: A normal reference [formula omitted]-norm based test

Abstract

A general linear hypothesis testing (GLHT) problem in heteroscedastic one-way MANOVA for high-dimensional data is considered and a normal reference L2-norm based test for the problem is proposed. Different from a few existing methodologies on the GLHT problem which impose strong assumptions on the underlying covariance matrices so that the associated tests’ null distributions are asymptotically normal, it is shown that under some regularity conditions, the proposed test statistic under the null hypothesis and a chi-square type mixture have the same normal or non-normal limiting distributions. It is then suggested to approximate the test’s null distribution using the distribution of the chi-square type mixture, which can be further approximated by the Welch–Satterthwaite chi-square-approximation with approximation parameters consistently estimated. Several simulation studies and a real data application are presented to demonstrate the good performance of the proposed test.