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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

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    1. 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.
    2. R. Dennis Cook & Bing Li & Francesca Chiaromonte, 2007. "Dimension reduction in regression without matrix inversion," Biometrika, Biometrika Trust, vol. 94(3), pages 569-584.
    3. Zhihua Su & R. Dennis Cook, 2011. "Partial envelopes for efficient estimation in multivariate linear regression," Biometrika, Biometrika Trust, vol. 98(1), pages 133-146.
    4. 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.
    5. 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.
    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. 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.
    3. 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).
    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. Alexander M. Franks, 2022. "Reducing subspace models for large‐scale covariance regression," Biometrics, The International Biometric Society, vol. 78(4), pages 1604-1613, December.
    6. 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).

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