Department of Mathematics
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
The research of Guangming Pan was partially supported by the Ministry of Education, Singapore, under grant ARC 14/11. Tiejun Tong’s research was supported by Hong Kong Research grant HKBU202711 and Hong Kong Baptist University FRG grants FRG2/11-12/110 and FRG1/13-14/018. Lixing Zhu’s research was supported by a grant from the Research Grants Council of Hong Kong and a Faculty Research Grant (FRG) from Hong Kong Baptist University. The authors thank the Editor, an associate editor, and two reviewers for their helpful comments and suggestions that have substantially improved an early version of this manuscript.
Link to Publisher's Edition
Wang, C., Pan, G., Tong, T., & Zhu, L. (2015). Shrinkage estimation of large dimensional precision matrix using random matrix theory. Statistica Sinica, 25 (3), 993-1008. https://doi.org/10.5705/ss.2012.328