Alignment and matching tests for high-dimensional tensor signals via tensor contraction
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915782086098944 |
|---|---|
| author | Liu, Ruihan Wang, Zhenggang Yao, Jianfeng |
| author_facet | Liu, Ruihan Wang, Zhenggang Yao, Jianfeng |
| contents | We consider two hypothesis testing problems for low-rank and high-dimensional tensor signals, namely the tensor signal alignment and tensor signal matching problems. These problems are challenging due to the high dimension of tensors and the lack of suitable test statistics. By exploiting a recent tensor contraction method, we propose and validate relevant test statistics using eigenvalues of a data matrix resulting from the tensor contraction. The matrix entries exhibit long-range dependence, which makes the analysis of the matrix challenging, involved, and distinct from standard random matrix theory. Our approach provides a novel framework for addressing hypothesis testing problems in the context of high-dimensional tensor signals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01732 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Alignment and matching tests for high-dimensional tensor signals via tensor contraction Liu, Ruihan Wang, Zhenggang Yao, Jianfeng Methodology Primary 62H15, secondary 60B20, 62H10 We consider two hypothesis testing problems for low-rank and high-dimensional tensor signals, namely the tensor signal alignment and tensor signal matching problems. These problems are challenging due to the high dimension of tensors and the lack of suitable test statistics. By exploiting a recent tensor contraction method, we propose and validate relevant test statistics using eigenvalues of a data matrix resulting from the tensor contraction. The matrix entries exhibit long-range dependence, which makes the analysis of the matrix challenging, involved, and distinct from standard random matrix theory. Our approach provides a novel framework for addressing hypothesis testing problems in the context of high-dimensional tensor signals. |
| title | Alignment and matching tests for high-dimensional tensor signals via tensor contraction |
| topic | Methodology Primary 62H15, secondary 60B20, 62H10 |
| url | https://arxiv.org/abs/2411.01732 |