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讲座简介：
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Controlling the false discovery rate (FDR) is a hot and challenging topic in the multiple hypothesis testing problems, especially for the high-dimensional regression models. In this paper, the main aim is to extend the knockoff idea to the high-dimensional regression models and meanwhile control the FDR. However, the singularity of the sample covariance matrix leads to the key problem that the knockoff variable cannot be directly constructed, and thus the knockoff filter also fails to control the FDR in the high-dimensional setting. To attack these problems, we propose a new proposal on knockoff filter, called as graphical knockoff filter, to consider the high-dimensional linear regression model with the Gaussian random design. We can obtain the efficient estimator of the precision matrix based on the estimation theory of ultra-large Gaussian graphical models, which can help us to construct the cheap knockoff variable beautifully as a control group in the high-dimensional setting. It is important that the graphical knockoff procedure can directly be used to select the significant variable with nonzero coefficients efficiently while bounding the FDR under the help of Lasso solution. The properties of the proposed graphical knockoff procedures are investigated both theoretically and numerically. It is shown that the proposed graphical knockoff procedure asymptotically controls the FDR at the target level $q$ and has the higher statistical power. Compared to the existing methods, simulation results show that the proposed graphical knockoff procedure performs well numerically in terms of both the empirical false discovery rate (eFDR) and power of the test. A real data is analyzed to assess the performance of the proposed graphical knockoff procedure. |
