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Title: High dimensional integrative analysis Authors:  Hongyuan Cao - University of Missouri-Columbia (United States) [presenting]
Abstract: Large scale multiple testing is a fundamental problem in high dimensional statistical inference. Recent technological advancement makes available various types of auxiliary information such as prior data and external covariates. Our goal is to use such auxiliary information to improve power in a tuning parameter free manner, compared to conventional procedures that only use test statistics or $p$-values. This is formally achieved through a shape-constrained relationship between auxiliary information and test statistics or $p$-values. We show that the proposed method leads to a large power increase, while controlling the false discovery rate, both empirically and theoretically. Extensive simulations demonstrate the advantage of the proposed method over several state-of-the-art methods. Dataset from GWAS and multiple-tissue eQTL analysis are used to illustrate this new methodology.