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Sufficient dimension reduction constrained through sub-populations

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  • Al-Najjar, Elias
  • Adragni, Kofi P.

Abstract

Most methodologies for sufficient dimension reduction (SDR) in regression are limited to continuous predictors, although many data sets do contain both continuous and categorical variables. Application of these methods to regressions that include qualitative predictors such as gender or species may be inappropriate. Regressions that include a set of qualitative predictors W in addition to a vector X of many-valued predictors and a response Y are considered. Using principal fitted components (PFC) models, a likelihood-based SDR method, a sufficient dimension reduction of X that is constrained through the sub-populations established by W is sought. An estimator of the sufficient reduction subspace is provided and its use is demonstrated through applications.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:111:y:2017:i:c:p:131-144
    DOI: 10.1016/j.csda.2017.02.008
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    References listed on IDEAS

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    1. 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.
    2. Kofi Placid Adragni, 2015. "Independent screening in high-dimensional exponential family predictors' space," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(2), pages 347-359, February.
    3. Li, Bing & Wang, Shaoli, 2007. "On Directional Regression for Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 997-1008, September.
    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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