High dimensional Gaussian copula graphical model with FDR control

Abstract

A multiple testing procedure is proposed to estimate the high dimensional Gaussian copula graphical model and nonparametric rank-based correlation coefficient estimators are exploited to construct the test statistics, which achieve modeling flexibility and estimation robustness. Compared to the existing methods depending on regularization technique, the proposed method avoids the ambiguous relationship between the regularized parameter and the number of false edges in graph estimation. It is proved that the proposed procedure can control the false discovery rate (FDR) asymptotically. Besides theoretical analysis, thorough numerical simulations are conducted to compare the graph estimation performance of the proposed method with some other state-of-the-art methods. The result shows that the proposed method works quite well under both non-Gaussian and Gaussian settings. The proposed method is then applied on a stock market data set to illustrate its empirical usefulness.