Estimating false discovery rate for high-dimensional multiple testing problems based on dependent test statistics is very important to scientific discovery and challenging to statistics. It varies from one realization to another. When the covariance matrix is known, Fan, Han and Gu (2012) proposed a principal factor approximation method to deal with an arbitrary dependence structure of test statistics. They derived an approximate formula for false discovery proportion (FDP), which depends on the covariance matrix of the test statistics. In many applications, however, the covariance matrix of test statistics is unknown and has to be estimated. The accuracy of estimated covariance matrix needed for accurately estimating FDP will be unveiled in this talk. In particular, it is shown that when the covariance admits an approximate factor structure, an estimate can be constructed to satisfy the required accuracy. The results will be illustrated by both simulation and real data applications.
(Joint work with Xu Han)