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Partial envelopes for efficient estimation in multivariate linear regression

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  • Zhihua Su
  • R. Dennis Cook

Abstract

We introduce the partial envelope model, which leads to a parsimonious method for multivariate linear regression when some of the predictors are of special interest. It has the potential to achieve massive efficiency gains compared with the standard model in the estimation of the coefficients for the selected predictors. The partial envelope model is a variation on the envelope model proposed by Cook et al. (2010) but, as it focuses on part of the predictors, it has looser restrictions and can further improve the efficiency. We develop maximum likelihood estimation for the partial envelope model and discuss applications of the bootstrap. An example is provided to illustrate some of its operating characteristics. Copyright 2011, Oxford University Press.

Suggested Citation

  • Zhihua Su & R. Dennis Cook, 2011. "Partial envelopes for efficient estimation in multivariate linear regression," Biometrika, Biometrika Trust, vol. 98(1), pages 133-146.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:1:p:133-146
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    File URL: http://hdl.handle.net/10.1093/biomet/asq063
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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. R. D. Cook & I. S. Helland & Z. Su, 2013. "Envelopes and partial least squares regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(5), pages 851-877, November.
    3. D. J. Eck & R. D. Cook, 2017. "Weighted envelope estimation to handle variability in model selection," Biometrika, Biometrika Trust, vol. 104(3), pages 743-749.
    4. Minji Lee & Zhihua Su, 2020. "A Review of Envelope Models," International Statistical Review, International Statistical Institute, vol. 88(3), pages 658-676, December.
    5. Li, Gen & Yang, Dan & Nobel, Andrew B. & Shen, Haipeng, 2016. "Supervised singular value decomposition and its asymptotic properties," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 7-17.
    6. Cook, R. Dennis & Forzani, Liliana & Su, Zhihua, 2016. "A note on fast envelope estimation," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 42-54.
    7. 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.
    8. Iaci, Ross & Yin, Xiangrong & Zhu, Lixing, 2016. "The Dual Central Subspaces in dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 178-189.
    9. Yeonhee Park & Zhihua Su & Hongtu Zhu, 2017. "Groupwise envelope models for imaging genetic analysis," Biometrics, The International Biometric Society, vol. 73(4), pages 1243-1253, December.
    10. 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.
    11. Cook, R. Dennis & Su, Zhihua & Yang, Yi, 2015. "envlp: A MATLAB Toolbox for Computing Envelope Estimators in Multivariate Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 62(i08).

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