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Shrinkage inverse regression estimation for model-free variable selection

Author

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  • Howard D. Bondell
  • Lexin Li

Abstract

The family of inverse regression estimators that was recently proposed by Cook and Ni has proven effective in dimension reduction by transforming the high dimensional predictor vector to its low dimensional projections. We propose a general shrinkage estimation strategy for the entire inverse regression estimation family that is capable of simultaneous dimension reduction and variable selection. We demonstrate that the new estimators achieve consistency in variable selection without requiring any traditional model, meanwhile retaining the root "n" estimation consistency of the dimension reduction basis. We also show the effectiveness of the new estimators through both simulation and real data analysis. Copyright (c) 2009 Royal Statistical Society.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jorssb:v:71:y:2009:i:1:p:287-299
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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9868.2008.00686.x
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Lexin Li, 2007. "Sparse sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 94(3), pages 603-613.
    3. Zhu, Yu & Zeng, Peng, 2006. "Fourier Methods for Estimating the Central Subspace and the Central Mean Subspace in Regression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1638-1651, December.
    4. Lexin Li & R. Dennis Cook & Christopher J. Nachtsheim, 2005. "Model-free variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 285-299.
    5. Ming Yuan & Yi Lin, 2007. "On the non-negative garrotte estimator," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 143-161.
    6. Lexin Li & Xiangrong Yin, 2008. "Sliced Inverse Regression with Regularizations," Biometrics, The International Biometric Society, vol. 64(1), pages 124-131, March.
    7. 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.
    8. R. Dennis Cook & Liqiang Ni, 2006. "Using intraslice covariances for improved estimation of the central subspace in regression," Biometrika, Biometrika Trust, vol. 93(1), pages 65-74, March.
    9. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67.
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    Citations

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    Cited by:

    1. Radchenko, Peter, 2015. "High dimensional single index models," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 266-282.
    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. Wenbin Lu & Lexin Li, 2011. "Sufficient Dimension Reduction for Censored Regressions," Biometrics, The International Biometric Society, vol. 67(2), pages 513-523, June.
    4. Wang, Tao & Xu, Pei-Rong & Zhu, Li-Xing, 2012. "Non-convex penalized estimation in high-dimensional models with single-index structure," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 221-235.
    5. repec:eee:stapro:v:128:y:2017:i:c:p:44-51 is not listed on IDEAS
    6. Wei Sun & Lexin Li, 2012. "Multiple Loci Mapping via Model-free Variable Selection," Biometrics, The International Biometric Society, vol. 68(1), pages 12-22, March.
    7. 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.
    8. 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.
    9. 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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