One-Way High-Dimensional ANOVA

Abstract

ANOVA is one of the most important tools in comparing the treatment means among different groups in repeated measurements. The classical $F$ test is routinely used to test if the treatment means are the same across different groups. However, it is inefficient when the number of groups or dimension gets large. We propose a smoothing truncation test to deal with this problem. It is shown theoretically and empirically that the proposed test works regardless of the dimension. The limiting null and alternative distributions of our test statistic are established for fixed and diverging number of treatments. Simulations demonstrate superior performance of the proposed test over the F test in different settings.