@article{1babbc2125894aa49f393c5fde6ce6f8,
title = "Bandwidth Selection for Large Covariance and Precision Matrices",
abstract = "For large covariance matrices and the corresponding precision matrices with banding structures, this paper develops a criterion to identify the bandwidth. The new method is based on an objective function that is discontinuous at the true bandwidth to show a {"}valley-cliff{"} pattern so that the identification of this location can be visualized and easily implemented. We offer the estimation consistency and the estimation error bound of the estimated covariance matrix and precision matrix with this estimated bandwidth. Numerical studies demonstrate the finite sample validity of the method, and a real data validity analysis is used for illustration.",
keywords = "Banding, Cholesky decomposition, Covariance matrix, Large p small n, Precision matrix, Tapering",
author = "Xuehu Zhu and Jian Guo and Xu Guo and Lixing Zhu and Jiasen Zheng",
note = "The authors are grateful to Drs. Songxi Chen, Yumou Qiu, and Baiguo Anfor providing partial codes. Xuehu Zhu's research was supported by the National Key R\&D Program of China (2022YFA1003803) , the National Social Science Foundation of China (21BTJ048) , and the Zhongying Young Scholar Program. Xu Guo's research was supported by a grant from the Natural Science Foundation of China (NSFC12071038) . The research of Lixing Zhu was supported by grants (NSFC12131006 and NSFC12471276) from the National Scientific Foundation of China and a grant (CI2023C063YLL) from the Scientific and Technological Innovation Project of China Academy of Chinese Medical Science.",
year = "2025",
month = jan,
doi = "10.5705/ss.202022.0337",
language = "English",
volume = "35",
pages = "321--341",
journal = "Statistica Sinica",
issn = "1017-0405",
publisher = "Institute of Statistical Science",
number = "1",
}
