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Sufficient dimension reduction for the conditional mean with a categorical predictor in multivariate regression

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  • Yoo, Jae Keun

Abstract

Recent sufficient dimension reduction methodologies in multivariate regression do not have direct application to a categorical predictor. For this, we define the multivariate central partial mean subspace and propose two methodologies to estimate it. The first method uses the ordinary least squares. Chi-squared distributed statistics for dimension tests are constructed, and an estimate of the target subspace is consistent and efficient. Moreover, the effects of continuous predictors can be tested without assuming any model. The second method extends Iterative Hessian Transformation to this context. For dimension estimation, permutation tests are used. Simulated and real data examples for illustrating various properties of the proposed methods are presented.

Suggested Citation

  • Yoo, Jae Keun, 2008. "Sufficient dimension reduction for the conditional mean with a categorical predictor in multivariate regression," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1825-1839, September.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:8:p:1825-1839
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    References listed on IDEAS

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    1. Jae Keun Yoo & R. Dennis Cook, 2007. "Optimal sufficient dimension reduction for the conditional mean in multivariate regression," Biometrika, Biometrika Trust, vol. 94(1), pages 231-242.
    2. Li K-C. & Aragon Y. & Shedden K. & Thomas Agnan C., 2003. "Dimension Reduction for Multivariate Response Data," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 99-109, January.
    3. 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.
    4. Cook, R. Dennis & Ni, Liqiang, 2005. "Sufficient Dimension Reduction via Inverse Regression: A Minimum Discrepancy Approach," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 410-428, June.
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    Cited by:

    1. Hilafu, Haileab & Yin, Xiangrong, 2013. "Sufficient dimension reduction in multivariate regressions with categorical predictors," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 139-147.
    2. Zhang, Hong-Fan, 2021. "Minimum Average Variance Estimation with group Lasso for the multivariate response Central Mean Subspace," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    3. Zhang, Yaowu & Zhu, Liping & Ma, Yanyuan, 2017. "Efficient dimension reduction for multivariate response data," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 187-199.

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