The Annals of Statistics· 2026Q1
Alignment and matching tests for high-dimensional tensor signals via tensor contraction
- 0citations
- Q1SCImago
- 2026year
Short summary
A novel framework using tensor contraction and eigenvalues of a data matrix is proposed for hypothesis testing of low-rank, high-dimensional tensor signals, addressing challenges from high dimensions and long-range dependence.
AI-generated from the title and abstract; the full text is not read.
Key points
- Proposes test statistics for tensor signal alignment and matching problems in high-dimensional, low-rank tensor signals.
- Employs a tensor contraction method to generate a data matrix from tensor signals.
- Uses eigenvalues of the data matrix as the basis for the test statistics.
- Addresses analytical challenges arising from the long-range dependence in the data matrix entries.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. The Annals of Statistics, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Computational Mathematics
Computational MathematicsMathematics