Control of the false discovery rate under arbitrary covariance dependence

Xu Han Weijie Gu Jianqing Fan

Statistics Theory and Methods mathscidoc:1912.43360

arXiv preprint arXiv:1012.4397, 2010.12
Multiple hypothesis testing is a fundamental problem in high dimensional inference, with wide applications in many scientific fields. In genome-wide association studies, tens of thousands of tests are performed simultaneously to find if any genes are associated with some traits and those tests are correlated. When test statistics are correlated, false discovery control becomes very challenging under arbitrary dependence. In the current paper, we propose a new methodology based on principal factor approximation, which successfully substracts the common dependence and weakens significantly the correlation structure, to deal with an arbitrary dependence structure. We derive the theoretical distribution for false discovery proportion (FDP) in large scale multiple testing when a common threshold is used and provide a consistent FDP. This result has important applications in controlling FDR and FDP. Our estimate of FDP compares favorably with Efron (2007)'s approach, as demonstrated by in the simulated examples. Our approach is further illustrated by some real data applications.
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@inproceedings{xu2010control,
  title={Control of the false discovery rate under arbitrary covariance dependence},
  author={Xu Han, Weijie Gu, and Jianqing Fan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113931081123920},
  booktitle={arXiv preprint arXiv:1012.4397},
  year={2010},
}
Xu Han, Weijie Gu, and Jianqing Fan. Control of the false discovery rate under arbitrary covariance dependence. 2010. In arXiv preprint arXiv:1012.4397. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113931081123920.
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