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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.<\/jats:p>","DOI":"10.1214\/26-aos2656","type":"journal-article","created":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T12:53:43Z","timestamp":1790945623000},"page":"2532-2559","source":"Crossref","is-referenced-by-count":0,"title":["Alignment and matching tests for high-dimensional tensor signals via tensor contraction"],"prefix":"10.1214","volume":"54","author":[{"given":"Ruihan","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Statistics and Actuarial Science, The University of Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhenggang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Statistics and Data Science, Southeast University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianfeng","family":"Yao","sequence":"additional","affiliation":[{"name":"School of Data Science, The Chinese University of Hong Kong (Shenzhen)"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"7","doi-asserted-by":"publisher","unstructured":"<small>Ben Arous, G.<\/small>, <small>Gheissari, R.<\/small> and <small>Jagannath, A.<\/small> (2020). 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