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

TL;DR

This paper introduces new threshold-based tests for fixed and random ANOVA that adaptively combine coordinatewise and blockwise thresholding to improve power under various alternative hypotheses.

Contribution

It develops novel thresholding-based tests for ANOVA that unify coordinatewise and blockwise approaches, enhancing flexibility and power.

Findings

Tests perform well under sparse and dense alternatives

Thresholding improves detection power in ANOVA

Method unifies coordinatewise and blockwise strategies

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.