Minimax estimation of covariance and precision matrices for high-dimensional time series with long-memory
| Autor: | Qihu Zhang, Cheolwoo Park, Jongik Chung |
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| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Estimation Series (mathematics) Open problem 010102 general mathematics High dimensional Covariance Minimax 01 natural sciences 010104 statistics & probability Long memory Convergence (routing) Applied mathematics 0101 mathematics Statistics Probability and Uncertainty Mathematics |
| Zdroj: | Statistics & Probability Letters. 177:109177 |
| ISSN: | 0167-7152 |
| DOI: | 10.1016/j.spl.2021.109177 |
| Popis: | 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). |
| Databáze: | OpenAIRE |
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