Title: Optimal threshold selection for covariance estimation
Authors: Yumou Qiu - Iowa State University (United States) [presenting]
Abstract: Thresholding is a regularization method commonly used for covariance estimation, which provides consistent estimators if the population covariance satisfies certain sparsity condition. However, the performance of the thresholding estimators heavily depends on the threshold level. By minimizing the Frobenius risk of the adaptive thresholding estimator for covariances, we conduct a theoretical study for the optimal threshold level, and obtain its analytical expression. A consistent estimator based on this expression is proposed for the optimal threshold level. Comparing to the state-of-art cross validation method, the proposed method is easy to implement and much more efficient in computation. Numerical simulations and a case study on gene expression data are conducted to illustrate the proposed method.