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Penalized principal logistic regression for sparse sufficient dimension reduction

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  • Shin, Seung Jun
  • Artemiou, Andreas

Abstract

Sufficient dimension reduction (SDR) is a successive tool for reducing the dimensionality of predictors by finding the central subspace, a minimal subspace of predictors that preserves all the regression information. When predictor dimension is large, it is often assumed that only a small number of predictors is informative. In this regard, sparse SDR is desired to achieve variable selection and dimension reduction simultaneously. We propose a principal logistic regression (PLR) as a new SDR tool and further develop its penalized version for sparse SDR. Asymptotic analysis shows that the penalized PLR enjoys the oracle property. Numerical investigation supports the advantageous performance of the proposed methods.

Suggested Citation

  • Shin, Seung Jun & Artemiou, Andreas, 2017. "Penalized principal logistic regression for sparse sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 48-58.
    • Handle: RePEc:eee:csdana:v:111:y:2017:i:c:p:48-58
    DOI: 10.1016/j.csda.2016.12.003
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    References listed on IDEAS

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    1. Lexin Li, 2007. "Sparse sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 94(3), pages 603-613.
    2. Howard D. Bondell & Lexin Li, 2009. "Shrinkage inverse regression estimation for model‐free variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 287-299, January.
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    4. Wang, Hansheng & Xia, Yingcun, 2008. "Sliced Regression for Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 811-821, June.
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    6. Hyonho Chun & Sündüz Keleş, 2010. "Sparse partial least squares regression for simultaneous dimension reduction and variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 3-25, January.
    7. 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.
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    Cited by:

    1. Pircalabelu, Eugen & Artemiou, Andreas, 2020. "The LassoPSVM approach for sufficient dimension reduction using principal projections," LIDAM Discussion Papers ISBA 2020008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Jang, Hyun Jung & Shin, Seung Jun & Artemiou, Andreas, 2023. "Principal weighted least square support vector machine: An online dimension-reduction tool for binary classification," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    3. Cadirci, Mehmet Siddik & Evans, Dafydd & Leonenko, Nikolai & Makogin, Vitalii, 2022. "Entropy-based test for generalised Gaussian distributions," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    4. Pircalabelu, Eugen & Artemiou, Andreas, 2021. "Graph informed sliced inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    5. Hayley Randall & Andreas Artemiou & Xingye Qiao, 2021. "Sufficient dimension reduction based on distance‐weighted discrimination," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1186-1211, December.

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