On the testing of multiple hypothesis in sliced inverse regression

TL;DR

This paper introduces a new model-free multiple testing procedure based on Angular Balanced Statistics for assessing predictor effects in sliced inverse regression, demonstrating improved power and controlled false discovery rate.

Contribution

The paper develops the Angular Balanced Statistic and a novel multiple testing method that is model-free, asymptotically valid, and more powerful than existing alternatives.

Findings

ABS is asymptotically symmetric under the null hypothesis.

The MTA procedure controls false discovery rate asymptotically.

Numerical results show MTA outperforms existing methods in power.

Abstract

We consider the multiple testing of the general regression framework aiming at studying the relationship between a univariate response and a p-dimensional predictor. To test the hypothesis of the effect of each predictor, we construct an Angular Balanced Statistic (ABS) based on the estimator of the sliced inverse regression without assuming a model of the conditional distribution of the response. According to the developed limiting distribution results in this paper, we have shown that ABS is asymptotically symmetric with respect to zero under the null hypothesis. We then propose a Model-free multiple Testing procedure using Angular balanced statistics (MTA) and show theoretically that the false discovery rate of this method is less than or equal to a designated level asymptotically. Numerical evidence has shown that the MTA method is much more powerful than its alternatives, subject to the control of the false discovery rate.