Local approximations of inverse block Toeplitz matrices and Baxter-type theorems for long-memory processes
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929379267837952 |
|---|---|
| author | Inoue, Akihiko Yang, Junho |
| author_facet | Inoue, Akihiko Yang, Junho |
| contents | We derive sharp approximation error bounds for inverse block Toeplitz matrices associated with multivariate long-memory stationary processes. The error bounds are evaluated for both column and row sums. These results are used to prove the strong convergence of the solutions of general block Toeplitz systems. A crucial part of the proof is to bound sums consisting of the Fourier coefficients of the phase function attached to the singular symbol of the Toeplitz matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_00470 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Local approximations of inverse block Toeplitz matrices and Baxter-type theorems for long-memory processes Inoue, Akihiko Yang, Junho Statistics Theory Probability We derive sharp approximation error bounds for inverse block Toeplitz matrices associated with multivariate long-memory stationary processes. The error bounds are evaluated for both column and row sums. These results are used to prove the strong convergence of the solutions of general block Toeplitz systems. A crucial part of the proof is to bound sums consisting of the Fourier coefficients of the phase function attached to the singular symbol of the Toeplitz matrices. |
| title | Local approximations of inverse block Toeplitz matrices and Baxter-type theorems for long-memory processes |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2304.00470 |