Browsing by Author "Xie, J"

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    False Discovery Rate Control for High-Dimensional Networks of Quantile Associations Conditioning on Covariates
    (2018-01-16) Xie, J; Li, Ruosha
    Motivated by the gene co-expression pattern analysis, we propose a novel squac statistic to infer quantile associations conditioning on covariates. It features enhanced flexibility in handling variables with both arbitrary distributions and complex association patterns conditioning on covariates. We first derive its asymptotic null distribution, and then develop a multiple testing procedure based on squac to simultaneously test the independence between one pair of variables conditioning on covariates for all p(p − 1)/2 pairs. Here, p is the length of the outcomes and could exceed the sample size. The testing procedure does not require resampling or perturbation, and thus is computationally efficient. We prove by theory and numerical experiments that the squac testing method asymptotically controls the false discovery rate (fdr). It outperforms all alternative methods when the complex association panterns exist. Applied to a gastric cancer data, the squac method estimated the gene co-expression networks of early and late stage patients. It identified more changes in the networks which are associated with cancer survivals. We extend our method to the case that both the length of the outcomes and the length of covariates exceed the sample size, and show that the asymptotic theory still holds.
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    Joint estimation of multiple high-dimensional precision matrices
    (Statistica Sinica, 2016-04-01) Cai, TT; Li, H; Liu, W; Xie, J
    Motivated by analysis of gene expression data measured in different tissues or disease states, we consider joint estimation of multiple precision matrices to effectively utilize the partially shared graphical structures of the corresponding graphs. The procedure is based on a weighted constrained l∞/l1 minimization, which can be effectively implemented by a second-order cone programming. Compared to separate estimation methods, the proposed joint estimation method leads to estimators converging to the true precision matrices faster. Under certain regularity conditions, the proposed procedure leads to an exact graph structure recovery with a probability tending to 1. Simulation studies show that the proposed joint estimation methods outperform other methods in graph structure recovery. The method is illustrated through an analysis of an ovarian cancer gene expression data. The results indicate that the patients with poor prognostic subtype lack some important links among the genes in the apoptosis pathway.