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Dimension selection in tensor decompositions and envelope models

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  • Zhang, Xin
  • Zhao, Wenbiao
  • Zhu, Lixing

Abstract

The statistical analysis of tensor-valued data has emerged as an area of increasing methodological focus. Tensor decomposition models and low-rank tensor regression models often assume that there exists a low-rank structure of the tensor data or tensor coefficient. Consistent selection of structural dimensions or tensor ranks constitutes a problem of significant theoretical and practical importance. This paper introduces a unified framework for addressing this challenge, applicable across multiple tensor decomposition frameworks and envelope regression models.

Suggested Citation

  • Zhang, Xin & Zhao, Wenbiao & Zhu, Lixing, 2026. "Dimension selection in tensor decompositions and envelope models," Journal of Multivariate Analysis, Elsevier, vol. 211(C).
    • Handle: RePEc:eee:jmvana:v:211:y:2026:i:c:s0047259x25001071
    DOI: 10.1016/j.jmva.2025.105512
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