Yumou Qiu
University of Nebraska Lincoln

Threshold selection for covariance learning

Covariance matrices play an important role in many statistical methods and applications. Thresholding is widely used in regularized covariance estimation. However, the learning performance heavily depends on a key tuning parameter, the threshold level. In this talk, we discuss the optimal threshold selection in two aspects of covariance learning: estimation and testing. In estimation, the optimal threshold is defined as the minimizer of the Frobenius risk of the adaptive thresholding estimator for covariance. A theoretical study for the optimal threshold level is conducted and its analytical expression is obtained. A consistent estimator for the optimal threshold level is proposed. Second, we consider testing the equality of two high-dimensional covariance matrices. In this case, the optimal threshold level is the one that maximizes the signal to noise ratio of the test, which is different from the optimal threshold level of the estimation. We propose a multi-thresholding test that is able to adaptively select the optimal threshold level and is shown to be more powerful than the existing tests in detecting sparse and weak differences between two covariance matrices.

Refreshments at 3:45pm in Snedecor 2101.