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A note on fast envelope estimation

Author

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  • Cook, R. Dennis
  • Forzani, Liliana
  • Su, Zhihua

Abstract

We propose a new algorithm for envelope estimation, along with a new n-consistent method for computing starting values. The new algorithm, which does not require optimization over a Grassmannian, is shown by simulation to be much faster and typically more accurate than the best existing algorithm proposed by Cook and Zhang (2016).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:150:y:2016:i:c:p:42-54
    DOI: 10.1016/j.jmva.2016.05.006
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    References listed on IDEAS

    as
    1. R. Dennis Cook & Xin Zhang, 2015. "Foundations for Envelope Models and Methods," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 599-611, June.
    2. Hongtu Zhu & Zakaria Khondker & Zhaohua Lu & Joseph G. Ibrahim, 2014. "Bayesian Generalized Low Rank Regression Models for Neuroimaging Phenotypes and Genetic Markers," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 977-990, September.
    3. R. Dennis Cook & Bing Li & Francesca Chiaromonte, 2007. "Dimension reduction in regression without matrix inversion," Biometrika, Biometrika Trust, vol. 94(3), pages 569-584.
    4. 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.
    5. Zhihua Su & R. Dennis Cook, 2011. "Partial envelopes for efficient estimation in multivariate linear regression," Biometrika, Biometrika Trust, vol. 98(1), pages 133-146.
    6. Kudraszow, Nadia L. & Maronna, Ricardo A., 2011. "Estimates of MM type for the multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1280-1292, October.
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    Citations

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    Cited by:

    1. May, Paul & Biesecker, Matthew & Rekabdarkolaee, Hossein Moradi, 2022. "Response envelopes for linear coregionalization models," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    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. Hu, Jianhua & Liu, Xiaoqian & Liu, Xu & Xia, Ningning, 2022. "Some aspects of response variable selection and estimation in multivariate linear regression," Journal of Multivariate Analysis, Elsevier, vol. 188(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. Alexander M. Franks, 2022. "Reducing subspace models for large‐scale covariance regression," Biometrics, The International Biometric Society, vol. 78(4), pages 1604-1613, December.

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