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Estimating central subspaces via inverse third moments

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  • Xiangrong Yin

Abstract

Modern graphical tools have enhanced our ability to learn many things from data directly. In recent years, dimension reduction has proven to be an effective tool for generating low-dimensional summary plots without appreciable loss of information. Some well-known inverse regression methods for dimension reduction such as sliced inverse regression (Li, 1991) and sliced average variance estimation (Cook & Weisberg, 1991) have been developed to estimate summary plots for regression and discriminant analysis. In this paper, we suggest a new method that makes use of inverse third moments. This method can find structure beyond that found by sliced inverse regression and sliced average variance estimation, particularly regression mixtures. Illustrative examples are presented. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • Xiangrong Yin, 2003. "Estimating central subspaces via inverse third moments," Biometrika, Biometrika Trust, vol. 90(1), pages 113-125, March.
    • Handle: RePEc:oup:biomet:v:90:y:2003:i:1:p:113-125
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    Cited by:

    1. Yongtao Guan & Hansheng Wang, 2010. "Sufficient dimension reduction for spatial point processes directed by Gaussian random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 367-387, June.
    2. Lu Li & Kai Tan & Xuerong Meggie Wen & Zhou Yu, 2023. "Variable-dependent partial dimension reduction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 521-541, June.
    3. Yin, Xiangrong & Cook, R. Dennis, 2006. "Dimension reduction via marginal high moments in regression," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 393-400, February.
    4. Yu, Zhou & Zhu, Lixing & Wen, Xuerong Meggie, 2012. "On model-free conditional coordinate tests for regressions," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 61-72.
    5. Li‐Ping Zhu & Li‐Xing Zhu, 2009. "On distribution‐weighted partial least squares with diverging number of highly correlated predictors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 525-548, April.
    6. Wenjuan Li & Wenying Wang & Jingsi Chen & Weidong Rao, 2023. "Aggregate Kernel Inverse Regression Estimation," Mathematics, MDPI, vol. 11(12), pages 1-10, June.
    7. Wei Luo, 2022. "On efficient dimension reduction with respect to the interaction between two response variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 269-294, April.

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