Abstract
In many practical applications, the structure of covariance matrix is often blurred due to random errors, making the estimation of covariance matrix very difficult particularly for high-dimensional data. In this article, we propose a regularization method for finding a possible banded Toeplitz structure for a given covariance matrix A (e.g., sample covariance matrix), which is usually an estimator of the unknown population covariance matrix Σ. We aim to find a matrix, say B, which is of banded Toeplitz structure, such that the Frobenius-norm discrepancy between B and A achieves the smallest in the whole class of banded Toeplitz structure matrices. As a result, the obtained Toeplitz structured matrix B recoveries the underlying structure behind Σ. Our simulation studies show that B is also more accurate than the sample covariance matrix A when estimating the covariance matrix Σ that has a banded Toeplitz structure. The studies also show that the proposed method works very well in regularization of covariance structure.
Original language | English |
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Title of host publication | Matrices, statistics andbBig data |
Subtitle of host publication | selected contributions from IWMS 2016 |
Editors | S. Ejaz Ahmed, Francisco Carvalho, Simo Puntanen |
Place of Publication | Springer, Cham |
Publisher | Springer Nature |
Pages | 111-125 |
Number of pages | 15 |
ISBN (Electronic) | 9783030175191 |
ISBN (Print) | 9783030175184 |
DOIs | |
Publication status | Published - 2019 |
Event | The 25th International Workshop on Matrices and Statistics - Madeira, Portugal Duration: 6 Jun 2016 → 9 Jun 2016 |
Conference
Conference | The 25th International Workshop on Matrices and Statistics |
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Abbreviated title | IWMS'2016 |
Country/Territory | Portugal |
City | Madeira |
Period | 6/06/16 → 9/06/16 |
Keywords
- Covariance matrix structure
- Frobenius norm
- Regularization
- Toeplitz structure