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Dimension reduction and predictor selection in semiparametric models

Author

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  • Zhou Yu
  • Liping Zhu
  • Heng Peng
  • Lixing Zhu

Abstract

Dimension reduction in semiparametric regressions includes construction of informative linear combinations and selection of contributing predictors. To reduce the predictor dimension in semiparametric regressions, we propose an ℓ 1 -minimization of sliced inverse regression with the Dantzig selector, and establish a non-asymptotic error bound for the resulting estimator. We also generalize the regularization concept to sliced inverse regression with an adaptive Dantzig selector. This ensures that all contributing predictors are selected with high probability, and that the resulting estimator is asymptotically normal even when the predictor dimension diverges to infinity. Numerical studies confirm our theoretical observations and demonstrate that our proposals are superior to existing estimators in terms of both dimension reduction and predictor selection. Copyright 2013, Oxford University Press.

Suggested Citation

  • Zhou Yu & Liping Zhu & Heng Peng & Lixing Zhu, 2013. "Dimension reduction and predictor selection in semiparametric models," Biometrika, Biometrika Trust, vol. 100(3), pages 641-654.
    • Handle: RePEc:oup:biomet:v:100:y:2013:i:3:p:641-654
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    File URL: http://hdl.handle.net/10.1093/biomet/ast005
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    Cited by:

    1. Xiao, Zhen & Zhang, Qi, 2022. "Dimension reduction for block-missing data based on sparse sliced inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    2. Girard, Stéphane & Lorenzo, Hadrien & Saracco, Jérôme, 2022. "Advanced topics in Sliced Inverse Regression," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Weng, Jiaying, 2022. "Fourier transform sparse inverse regression estimators for sufficient variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    4. 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.
    5. Radchenko, Peter, 2015. "High dimensional single index models," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 266-282.
    6. Tan, Xin Lu, 2019. "Optimal estimation of slope vector in high-dimensional linear transformation models," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 179-204.
    7. Hojin Yang & Hongtu Zhu & Joseph G. Ibrahim, 2018. "MILFM: Multiple index latent factor model based on high‐dimensional features," Biometrics, The International Biometric Society, vol. 74(3), pages 834-844, September.

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