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Sufficient dimension reduction and variable selection for regression mean function with two types of predictors

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  • Wang, Qin
  • Yin, Xiangrong

Abstract

In this article, for the regression mean function of Y on , where Y is a scalar, is a px1 vector and W is a categorical variable, we propose a method, partial sparse MAVE, to achieve sufficient dimension reduction and variable selection on simultaneously. The method relaxes any particular distribution assumption on the model and on . We also extend this method to multivariate response of , and GPLSIM [Carroll, R.J., Fan, J., Gijbels, I., Wand, M.P., 1997. Generalized partially linear single-index models. Journal of the American Statistical Association 92, 477-489]. Simulations and a real data analysis confirm the efficacy of our method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:16:p:2798-2803
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    References listed on IDEAS

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    1. 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.
    2. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    3. 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.
    4. Lexin Li, 2007. "Sparse sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 94(3), pages 603-613.
    5. Ye Z. & Weiss R.E., 2003. "Using the Bootstrap to Select One of a New Class of Dimension Reduction Methods," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 968-979, January.
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    Cited by:

    1. 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.

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