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Envelopes and reduced-rank regression

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  • R. Dennis Cook
  • Liliana Forzani
  • Xin Zhang

Abstract

We incorporate the nascent idea of envelopes (Cook et al., Statist. Sinica 20, 927–1010) into reduced-rank regression by proposing a reduced-rank envelope model, which is a hybrid of reduced-rank and envelope regressions. The proposed model has total number of parameters no more than either of reduced-rank regression or envelope regression. The resulting estimator is at least as efficient as both existing estimators. The methodology of this paper can be adapted to other envelope models, such as partial envelopes (Su & Cook, Biometrika 98, 133–46) and envelopes in predictor space (Cook et al., J. R. Statist. Soc. B 75, 851–77).

Suggested Citation

  • R. Dennis Cook & Liliana Forzani & Xin Zhang, 2015. "Envelopes and reduced-rank regression," Biometrika, Biometrika Trust, vol. 102(2), pages 439-456.
    • Handle: RePEc:oup:biomet:v:102:y:2015:i:2:p:439-456.
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    File URL: http://hdl.handle.net/10.1093/biomet/asv001
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    Citations

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    Cited by:

    1. Zhang, Xin & Wang, Chong & Wu, Yichao, 2018. "Functional envelope for model-free sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 37-50.
    2. Minji Lee & Zhihua Su, 2020. "A Review of Envelope Models," International Statistical Review, International Statistical Institute, vol. 88(3), pages 658-676, December.
    3. Dennis Cook, R. & Forzani, Liliana, 2023. "On the role of partial least squares in path analysis for the social sciences," Journal of Business Research, Elsevier, vol. 167(C).
    4. 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.
    5. Guo, Wenxing & Balakrishnan, Narayanaswamy & He, Mu, 2023. "Envelope-based sparse reduced-rank regression for multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    6. Luo, Chongliang & Liang, Jian & Li, Gen & Wang, Fei & Zhang, Changshui & Dey, Dipak K. & Chen, Kun, 2018. "Leveraging mixed and incomplete outcomes via reduced-rank modeling," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 378-394.
    7. 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.

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