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A note on shrinkage sliced inverse regression

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  • Liqiang Ni
  • R. Dennis Cook
  • Chih-Ling Tsai

Abstract

We employ Lasso shrinkage within the context of sufficient dimension reduction to obtain a shrinkage sliced inverse regression estimator, which provides easier interpretations and better prediction accuracy without assuming a parametric model. The shrinkage sliced inverse regression approach can be employed for both single-index and multiple-index models. Simulation studies suggest that the new estimator performs well when its tuning parameter is selected by either the Bayesian information criterion or the residual information criterion. Copyright 2005, Oxford University Press.

Suggested Citation

  • Liqiang Ni & R. Dennis Cook & Chih-Ling Tsai, 2005. "A note on shrinkage sliced inverse regression," Biometrika, Biometrika Trust, vol. 92(1), pages 242-247, March.
    • Handle: RePEc:oup:biomet:v:92:y:2005:i:1:p:242-247
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    File URL: http://hdl.handle.net/10.1093/biomet/92.1.242
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    Cited by:

    1. Zou, Changliang & Chen, Xin, 2012. "On the consistency of coordinate-independent sparse estimation with BIC," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 248-255.
    2. Wang, Tao & Zhu, Lixing, 2013. "Sparse sufficient dimension reduction using optimal scoring," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 223-232.
    3. Heng-Hui Lue & Bing-Ran You, 2013. "High-dimensional regression analysis with treatment comparisons," Computational Statistics, Springer, vol. 28(3), pages 1299-1317, June.
    4. Li, Lexin & Yin, Xiangrong, 2009. "Longitudinal data analysis using sufficient dimension reduction method," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4106-4115, October.
    5. Zhu, Li-Ping & Zhu, Li-Xing, 2009. "Nonconcave penalized inverse regression in single-index models with high dimensional predictors," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 862-875, May.
    6. Bilin Zeng & Xuerong Meggie Wen & Lixing Zhu, 2017. "A link-free sparse group variable selection method for single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2388-2400, October.
    7. 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.
    8. Li-Ping Zhu & Lin-Yi Qian & Jin-Guan Lin, 2011. "Variable selection in a class of single-index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(6), pages 1277-1293, December.
    9. Girard, Stéphane & Lorenzo, Hadrien & Saracco, Jérôme, 2022. "Advanced topics in Sliced Inverse Regression," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    10. Weng, Jiaying, 2022. "Fourier transform sparse inverse regression estimators for sufficient variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    11. Moradi Rekabdarkolaee, Hossein & Wang, Qin, 2017. "Variable selection through adaptive MAVE," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 44-51.
    12. Zhou Yu & Yuexiao Dong & Li-Xing Zhu, 2016. "Trace Pursuit: A General Framework for Model-Free Variable Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 813-821, April.
    13. Wang, Qin & Yin, Xiangrong, 2008. "Sufficient dimension reduction and variable selection for regression mean function with two types of predictors," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2798-2803, November.
    14. Radchenko, Peter, 2015. "High dimensional single index models," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 266-282.
    15. Fang, Fang & Yu, Zhou, 2020. "Model averaging assisted sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    16. Wang, Qin & Yin, Xiangrong, 2008. "A nonlinear multi-dimensional variable selection method for high dimensional data: Sparse MAVE," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4512-4520, May.
    17. Yoo, Jae Keun, 2013. "Advances in seeded dimension reduction: Bootstrap criteria and extensions," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 70-79.
    18. Yao, Weixin & Wang, Qin, 2013. "Robust variable selection through MAVE," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 42-49.

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