Blockwise and coordinatewise thresholding to combine tests of different natures in modern ANOVA

Abstract

We derive new tests for fixed and random ANOVA based on a thresholded point estimate. The pivotal quantity is the threshold that sets all the coefficients of the null hypothesis to zero. Thresholding can be employed coordinatewise or blockwise, or both, which leads to tests with good power properties under alternative hypotheses that are either sparse or dense.