IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v211y2026ics0047259x25001071.html

Dimension selection in tensor decompositions and envelope models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X25001071
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2025.105512?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Tianqi Liu & Ming Yuan & Hongyu Zhao, 2022. "Characterizing Spatiotemporal Transcriptome of the Human Brain Via Low-Rank Tensor Decomposition," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 14(3), pages 485-513, December.
    2. Lexin Li & Xin Zhang, 2017. "Parsimonious Tensor Response Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1131-1146, July.
    3. Hua Zhou & Lexin Li & Hongtu Zhu, 2013. "Tensor Regression with Applications in Neuroimaging Data Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 540-552, June.
    4. Xiaoshan Li & Da Xu & Hua Zhou & Lexin Li, 2018. "Tucker Tensor Regression and Neuroimaging Analysis," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 520-545, December.
    5. J. Carroll & Jih-Jie Chang, 1970. "Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition," Psychometrika, Springer;The Psychometric Society, vol. 35(3), pages 283-319, September.
    6. Ledyard Tucker, 1966. "Some mathematical notes on three-mode factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 279-311, September.
    7. Anru Zhang & Rungang Han, 2019. "Optimal Sparse Singular Value Decomposition for High-Dimensional High-Order Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1708-1725, October.
    8. Zhu, Xuehu & Guo, Xu & Wang, Tao & Zhu, Lixing, 2020. "Dimensionality determination: A thresholding double ridge ratio approach," Computational Statistics & Data Analysis, Elsevier, vol. 146(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Su, Haiyue & Xia, Zhiming & Shang, Wenyuan & Shi, Meili, 2026. "Change-point detection in Vector-Tensor linear model," Statistics & Probability Letters, Elsevier, vol. 228(C).
    2. Xiumin Liu & Lu Niu & Junlong Zhao, 2023. "Statistical inference on the significance of rows and columns for matrix-valued data in an additive model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(3), pages 785-828, September.
    3. Bo Wei & Limin Peng & Ying Guo & Amita Manatunga & Jennifer Stevens, 2023. "Tensor response quantile regression with neuroimaging data," Biometrics, The International Biometric Society, vol. 79(3), pages 1947-1958, September.
    4. Ghannam, Mai & Nkurunziza, Sévérien, 2023. "Tensor Stein-rules in a generalized tensor regression model," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    5. Monica Billio & Roberto Casarin & Matteo Iacopini & Sylvia Kaufmann, 2023. "Bayesian Dynamic Tensor Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(2), pages 429-439, April.
    6. Xuejuan Zhang & Jinling Zhao, 2025. "An extrapolation trust-region alternating least-squares algorithm for triple decomposition of third-order tensors," Annals of Operations Research, Springer, vol. 349(3), pages 1933-1955, June.
    7. Zhichuan Zhu & Jingxiang Huang & Niansheng Tang, 2025. "Bayesian inference approaches for tensor quantile regression and its application," Statistical Papers, Springer, vol. 66(7), pages 1-37, December.
    8. Rungang Han & Yuetian Luo & Miaoyan Wang & Anru R. Zhang, 2022. "Exact clustering in tensor block model: Statistical optimality and computational limit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1666-1698, November.
    9. Mariela González-Narváez & María José Fernández-Gómez & Susana Mendes & José-Luis Molina & Omar Ruiz-Barzola & Purificación Galindo-Villardón, 2021. "Study of Temporal Variations in Species–Environment Association through an Innovative Multivariate Method: MixSTATICO," Sustainability, MDPI, vol. 13(11), pages 1-25, May.
    10. Henk Kiers, 1991. "Hierarchical relations among three-way methods," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 449-470, September.
    11. Dengdeng Yu & Matthew Pietrosanu & Ivan Mizera & Bei Jiang & Linglong Kong & Wei Tu, 2025. "Functional Linear Partial Quantile Regression with Guaranteed Convergence for Neuroimaging Data Analysis," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 17(1), pages 174-190, April.
    12. Willem Kloot & Pieter Kroonenberg, 1985. "External analysis with three-mode principal component models," Psychometrika, Springer;The Psychometric Society, vol. 50(4), pages 479-494, December.
    13. Elisa Frutos-Bernal & Ángel Martín del Rey & Irene Mariñas-Collado & María Teresa Santos-Martín, 2022. "An Analysis of Travel Patterns in Barcelona Metro Using Tucker3 Decomposition," Mathematics, MDPI, vol. 10(7), pages 1-17, March.
    14. Yoshio Takane & Forrest Young & Jan Leeuw, 1977. "Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 42(1), pages 7-67, March.
    15. Kim, Jonathan & Sandri, Brian J. & Rao, Raghavendra B. & Lock, Eric F., 2023. "Bayesian predictive modeling of multi-source multi-way data," Computational Statistics & Data Analysis, Elsevier, vol. 186(C).
    16. Serrano Cinca, C. & Mar Molinero, C. & Gallizo Larraz, J.L., 2005. "Country and size effects in financial ratios: A European perspective," Global Finance Journal, Elsevier, vol. 16(1), pages 26-47, August.
    17. Giuseppe Brandi & Ruggero Gramatica & Tiziana Di Matteo, 2019. "Unveil stock correlation via a new tensor-based decomposition method," Papers 1911.06126, arXiv.org, revised Apr 2020.
    18. Kai Deng & Xin Zhang, 2022. "Tensor envelope mixture model for simultaneous clustering and multiway dimension reduction," Biometrics, The International Biometric Society, vol. 78(3), pages 1067-1079, September.
    19. Wilderjans, Tom & Ceulemans, Eva & Van Mechelen, Iven, 2009. "Simultaneous analysis of coupled data blocks differing in size: A comparison of two weighting schemes," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1086-1098, February.
    20. Lan Liu & Wei Li & Zhihua Su & Dennis Cook & Luca Vizioli & Essa Yacoub, 2022. "Efficient estimation via envelope chain in magnetic resonance imaging‐based studies," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 481-501, June.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:211:y:2026:i:c:s0047259x25001071. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.