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A slice of multivariate dimension reduction

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  • Cook, R. Dennis

Abstract

We describe how many dimension reduction strategies are connected conceptually and philosophically, paving the way for a unified approach to multivariate dimension reduction in statistics. Specific methods covered include envelopes, sufficient dimension reduction methods like SIR and SAVE, principal components, principal fitted components, and partial least squares.

Suggested Citation

  • Cook, R. Dennis, 2022. "A slice of multivariate dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:jmvana:v:188:y:2022:i:c:s0047259x21000907
    DOI: 10.1016/j.jmva.2021.104812
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    References listed on IDEAS

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    1. Xiangrong Yin & R. Dennis Cook, 2002. "Dimension reduction for the conditional kth moment in regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 159-175, May.
    2. Michael E. Tipping & Christopher M. Bishop, 1999. "Probabilistic Principal Component Analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 611-622.
    3. Yin, Xiangrong & Li, Bing & Cook, R. Dennis, 2008. "Successive direction extraction for estimating the central subspace in a multiple-index regression," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1733-1757, September.
    4. Artemiou, Andreas & Li, Bing, 2013. "Predictive power of principal components for single-index model and sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 176-184.
    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. Li, Baibing & Hassel, Per A. & Morris, A. Julian & Martin, Elaine B., 2005. "A non-linear nested partial least-squares algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 48(1), pages 87-101, January.
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    Cited by:

    1. Cook, R. Dennis & Forzani, Liliana & Liu, Lan, 2023. "Partial least squares for simultaneous reduction of response and predictor vectors in regression," Journal of Multivariate Analysis, Elsevier, vol. 196(C).

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