Testing Homogeneity in a heteroscedastic contaminated normal mixture
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 -scores derived from the individual -tests and then use this model to control the false discovery rate. We propose a new class of contaminated normal mixtures for modelling -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.
Cite
@article{arxiv.2507.15630,
title = {Testing Homogeneity in a heteroscedastic contaminated normal mixture},
author = {Xiaoqing Niu and Pengfei Li and Yuejiao Fu},
journal= {arXiv preprint arXiv:2507.15630},
year = {2025}
}