Department of Mathematics
Shrinkage estimation of large dimensional precision matrix using random matrix theory
This paper considers ridge-type shrinkage estimation of a large dimensional precision matrix. The asymptotic optimal shrinkage coefficients and the theoretical loss are derived. Data-driven estimators for the shrinkage coefficients are also conducted based on the asymptotic results from random matrix theory. The new method is distribution-free and no assumption on the structure of the covariance matrix or the precision matrix is required. The proposed method also applies to situations where the dimension is larger than the sample size. Numerical studies of simulated and real data demonstrate that the proposed estimator performs better than existing competitors in a wide range of settings.
Large dimensional data, Precision matrix, Random matrix theory, Ridge-type estimator, Shrinkage estimation
Source Publication Title
Academia Sinica, Institute of Statistical Science
Wang, Cheng, Guangming Pan, Tiejun Tong, and Lixing Zhu. "Shrinkage estimation of large dimensional precision matrix using random matrix theory." Statistica Sinica 25.3 (2015): 993-1008.