Testing Homogeneity in a heteroscedastic contaminated normal mixture
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911067580399616 |
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| author | Niu, Xiaoqing Li, Pengfei Fu, Yuejiao |
| author_facet | Niu, Xiaoqing Li, Pengfei Fu, Yuejiao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15630 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Testing Homogeneity in a heteroscedastic contaminated normal mixture Niu, Xiaoqing Li, Pengfei Fu, Yuejiao Methodology 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. |
| title | Testing Homogeneity in a heteroscedastic contaminated normal mixture |
| topic | Methodology |
| url | https://arxiv.org/abs/2507.15630 |