Efficient nonparametric estimation of Toeplitz covariance matrices

• 成果类型: Article
• 署名作者: Klockmann, K.; Krivobokova, T.
• 署名单位: University of Vienna
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asae002
• 发表日期: 2024
• 页码: 843864
• 关键词: autocovariance matrices; smoothing parameter; spectral density

摘要

A new efficient nonparametric estimator for Toeplitz covariance matrices is proposed. This estimator is based on a data transformation that translates the problem of Toeplitz covariance matrix estimation to the problem of mean estimation in an approximate Gaussian regression. The resulting Toeplitz covariance matrix estimator is positive definite by construction, fully data driven and computationally very fast. Moreover, this estimator is shown to be minimax optimal under the spectral norm for a large class of Toeplitz matrices. These results are readily extended to estimation of inverses of Toeplitz covariance matrices. Also, an alternative version of the Whittle likelihood for the spectral density based on the discrete cosine transform is proposed.