Minimax estimation of covariance and precision matrices for high-dimensional time series with long-memory

This paper concerns the minimax estimation of covariance and precision matrices for high-dimensional time series with long-memory property. We generalize the minimax results for the convergence rates of the estimation of covariance matrices in Shu and Nan (2019) in several directions with a mild assumption, which was mentioned as an open problem in Supplement to Cai and Zhou (2012) for i.i.d. data. We also obtain the minimax results for the convergence rates of the estimation of precision matrices under various norms, which is not considered by Shu and Nan (2019) and Cai and Zhou (2012). (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper focuses on the minimax estimation of covariance and precision matrices for high-dimensional time series with long-memory property. The authors generalize and extend the results for the convergence rates of covariance matrix estimation in various directions under a mild assumption, which was previously mentioned as an open problem in existing literature. Additionally, the minimax results for the convergence rates of precision matrix estimation under different norms are obtained, which were not considered in previous studies.