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Sufficient dimension reduction in regressions across heterogeneous subpopulations

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  • Liqiang Ni
  • R. Dennis Cook

Abstract

Summary. Sliced inverse regression is one of the widely used dimension reduction methods. Chiaromonte and co‐workers extended this method to regressions with qualitative predictors and developed a method, partial sliced inverse regression, under the assumption that the covariance matrices of the continuous predictors are constant across the levels of the qualitative predictor. We extend partial sliced inverse regression by removing the restrictive homogeneous covariance condition. This extension, which significantly expands the applicability of the previous methodology, is based on a new estimation method that makes use of a non‐linear least squares objective function.

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  • Liqiang Ni & R. Dennis Cook, 2006. "Sufficient dimension reduction in regressions across heterogeneous subpopulations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 89-107, February.
    • Handle: RePEc:bla:jorssb:v:68:y:2006:i:1:p:89-107
    DOI: 10.1111/j.1467-9868.2005.00534.x
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    Cited by:

    1. Al-Najjar, Elias & Adragni, Kofi P., 2017. "Sufficient dimension reduction constrained through sub-populations," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 131-144.
    2. 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.

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