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A sparse eigen-decomposition estimation in semiparametric regression

  • Zhu, Li-Ping
  • Yu, Zhou
  • Zhu, Li-Xing
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    For semiparametric models, one of the key issues is to reduce the predictors' dimension so that the regression functions can be efficiently estimated based on the low-dimensional projections of the original predictors. Many sufficient dimension reduction methods seek such principal projections by conducting the eigen-decomposition technique on some method-specific candidate matrices. In this paper, we propose a sparse eigen-decomposition strategy by shrinking small sample eigenvalues to zero. Different from existing methods, the new method can simultaneously estimate basis directions and structural dimension of the central (mean) subspace in a data-driven manner. The oracle property of our estimation procedure is also established. Comprehensive simulations and a real data application are reported to illustrate the efficacy of the new proposed method.

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    File URL: http://www.sciencedirect.com/science/article/B6V8V-4XGGTDR-1/2/8494568d60c5985bd9fed489c71b0345
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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 54 (2010)
    Issue (Month): 4 (April)
    Pages: 976-986

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    Handle: RePEc:eee:csdana:v:54:y:2010:i:4:p:976-986
    Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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    1. 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.
    2. Bura E. & Cook R.D., 2001. "Extending Sliced Inverse Regression: the Weighted Chi-Squared Test," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 996-1003, September.
    3. 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.
    4. 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.
    5. 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.
    6. Peng Zeng, 2008. "Determining the dimension of the central subspace and central mean subspace," Biometrika, Biometrika Trust, vol. 95(2), pages 469-479.
    7. Yin, Xiangrong & Li, Bing & Cook, R. Dennis, 2008. "Successive direction extraction for estimating the central subspace in a multiple-index regression," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1733-1757, September.
    8. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
    9. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    10. Zhu, Li-Ping & Zhu, Li-Xing, 2007. "On kernel method for sliced average variance estimation," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 970-991, May.
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