IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v80y2018i2p387-408.html
   My bibliography  Save this article

Matrix variate regressions and envelope models

Author

Listed:
  • Shanshan Ding
  • R. Dennis Cook

Abstract

Modern technology often generates data with complex structures in which both response and explanatory variables are matrix valued. Existing methods in the literature can tackle matrix‐valued predictors but are rather limited for matrix‐valued responses. We study matrix variate regressions for such data, where the response Y on each experimental unit is a random matrix and the predictor X can be either a scalar, a vector or a matrix, treated as non‐stochastic in terms of the conditional distribution Y|X. We propose models for matrix variate regressions and then develop envelope extensions of these models. Under the envelope framework, redundant variation can be eliminated in estimation and the number of parameters can be notably reduced when the matrix variate dimension is large, possibly resulting in significant gains in efficiency. The methods proposed are applicable to high dimensional settings.

Suggested Citation

  • Shanshan Ding & R. Dennis Cook, 2018. "Matrix variate regressions and envelope models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(2), pages 387-408, March.
    • Handle: RePEc:bla:jorssb:v:80:y:2018:i:2:p:387-408
    DOI: 10.1111/rssb.12247
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/rssb.12247
    Download Restriction: no
    File URL: https://libkey.io/10.1111/rssb.12247?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Žikica Lukić & Bojana Milošević, 2024. "A novel two-sample test within the space of symmetric positive definite matrix distributions and its application in finance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(5), pages 797-820, October.
    2. 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.
    3. Minji Lee & Zhihua Su, 2020. "A Review of Envelope Models," International Statistical Review, International Statistical Institute, vol. 88(3), pages 658-676, December.
    4. Jain Yashita & Ding Shanshan & Qiu Jing, 2019. "Sliced inverse regression for integrative multi-omics data analysis," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 18(1), pages 1-13, February.
    5. Wei Hu & Tianyu Pan & Dehan Kong & Weining Shen, 2021. "Nonparametric matrix response regression with application to brain imaging data analysis," Biometrics, The International Biometric Society, vol. 77(4), pages 1227-1240, December.
    6. Yue Zhao & Ingrid Van Keilegom & Shanshan Ding, 2022. "Envelopes for censored quantile regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1562-1585, December.
    7. Federico Ferraccioli & Giovanna Menardi, 2023. "Modal clustering of matrix-variate data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 323-345, June.
    8. Wang, Di & Zheng, Yao & Li, Guodong, 2024. "High-dimensional low-rank tensor autoregressive time series modeling," Journal of Econometrics, Elsevier, vol. 238(1).

    More about this item

    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:bla:jorssb:v:80:y:2018:i:2:p:387-408. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    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.