Journal
JOURNAL OF APPLIED STATISTICS
Volume 46, Issue 8, Pages 1478-1491Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/02664763.2018.1552668
Keywords
Computer experiment; heteroscedastic contaminated normal model; homogeneity test; likelihood ratio test; EM-test
Categories
Funding
- Natural Sciences and Engineering Research Council of Canada (NSERC) [RGPIN 2018 05846]
- NSERC [RGPIN 2015 06592]
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Large-scale simultaneous hypothesis testing appears in many areas. 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 heteroscedastic contaminated normal mixture to describe the distribution of z-scores and design an EM-test for testing homogeneity in this class of mixture models. The proposed EM-test can be used to investigate whether a collection of z-scores has arisen from a single normal distribution or whether a heteroscedastic contaminated normal mixture is more appropriate. 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 analysed to exemplify the application of the proposed method.
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