An $\boldsymbol{L^{2}}$-norm based test for high-dimensional two-way MANOVA
Bu Zhou, Jin‐Ting Zhang, Guo Jia · Scientia Sinica Mathematica · 2020
In this paper, we propose and study an $L^{2}$-norm based test for high-dimensional two-way MANOVA where there are fewer observations than the dimension. The test statistic is constructed by removing the inverse sample covariance matrix in the Wald-type statistic for the general linear hypothesis.We propose to approximate the null distribution of our test statistic by using the well-known Welch-Satterthwaite chi-squared approximation and discuss the relationship between chi-squared approximation and the commonly-used normal approximation. The $L^{2}$-norm based test is also shown to admit several invariant properties under certain transformations. The asymptotic and approximate powers of the proposed test are investigated. Simulation studies and real data applications show that the proposed test performs well for high-dimensional data.