Testing Homogeneity in a heteroscedastic contaminated normal mixture

TL;DR

This paper introduces a new contaminated normal mixture model for $z$-scores in large-scale hypothesis testing, along with an EM-test for homogeneity, demonstrating improved power and accurate error control through simulations and real data analysis.

Contribution

It proposes a novel contaminated normal mixture model and an EM-test for homogeneity, enhancing detection power in large-scale testing scenarios.

Findings

The EM-test statistic follows a shifted mixture of chi-squared distribution.

The proposed method maintains accurate type I error rates.

It shows significantly higher power than existing methods in simulations.

Abstract

Large-scale simultaneous hypothesis testing appears in many areas such as microarray studies, genome-wide association studies, brain imaging, disease mapping and astronomical surveys. A well-known inference method is to control the false discovery rate. One popular approach is to model the $z$-scores derived from the individual $t$-tests and then use this model to control the false discovery rate. We propose a new class of contaminated normal mixtures for modelling $z$-scores. We further design an EM-test for testing homogeneity in this class of mixture models. We show that the EM-test statistic has a shifted mixture of chi-squared limiting distribution. Simulation results show that the proposed testing procedure has accurate type I error and significantly larger power than its competitors under a variety of model specifications. A real-data example is analyzed to exemplify the application of the proposed method.