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Weighted envelope estimation to handle variability in model selection

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  • D. J. Eck
  • R. D. Cook

Abstract

SummaryEnvelope methodology can provide substantial efficiency gains in multivariate statistical problems, but in some applications the estimation of the envelope dimension can induce selection volatility that may mitigate those gains. Current envelope methodology does not account for the added variance that can result from this selection. In this article, we circumvent dimension selection volatility through the development of a weighted envelope estimator. Theoretical justification is given for our estimator, and the validity of the residual bootstrap for estimating its asymptotic variance is established. A simulation study and real-data analysis illustrate the utility of our weighted envelope estimator.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:104:y:2017:i:3:p:743-749.
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    File URL: http://hdl.handle.net/10.1093/biomet/asx035
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    References listed on IDEAS

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    1. Z. Su & G. Zhu & X. Chen & Y. Yang, 2016. "Sparse envelope model: efficient estimation and response variable selection in multivariate linear regression," Biometrika, Biometrika Trust, vol. 103(3), pages 579-593.
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    3. Hjort N.L. & Claeskens G., 2003. "Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 879-899, January.
    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. Kenneth P. Burnham & David R. Anderson, 2004. "Multimodel Inference," Sociological Methods & Research, , vol. 33(2), pages 261-304, November.
    6. 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.
    7. Bradley Efron, 2014. "Estimation and Accuracy After Model Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 991-1007, September.
    8. Zhihua Su & R. Dennis Cook, 2011. "Partial envelopes for efficient estimation in multivariate linear regression," Biometrika, Biometrika Trust, vol. 98(1), pages 133-146.
    9. Liang, Hua & Zou, Guohua & Wan, Alan T. K. & Zhang, Xinyu, 2011. "Optimal Weight Choice for Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1053-1066.
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    Cited by:

    1. Minji Lee & Zhihua Su, 2020. "A Review of Envelope Models," International Statistical Review, International Statistical Institute, vol. 88(3), pages 658-676, December.
    2. 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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