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A data-adaptive hybrid method for dimension reduction

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  • Li-Ping Zhu
  • Li-Xing Zhu

Abstract

To gain the advantages of different inverse regression methods, the convex combination can be useful for estimating the central subspace. To select an appropriate combination coefficient in the hybrid method, we propose in this paper a data-adaptive hybrid method using the trace of kernel matrices. For ease of illustration, we consider particularly the combination of inverse regressions using the conditional mean and the conditional variance, both of which are separately powerful in estimating different models. Because the efficacy of the slicing estimation may deteriorate when it is used to estimate the conditional variance, we use the kernel smoother instead. The asymptotic normality at the root-n rate is achieved even with the data-driven combination weight. Illustrative examples by simulations and an application to horse mussel data is presented to demonstrate the necessity of the hybrid models and the efficacy of our kernel estimation.

Suggested Citation

  • Li-Ping Zhu & Li-Xing Zhu, 2009. "A data-adaptive hybrid method for dimension reduction," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(7), pages 851-861.
    • Handle: RePEc:taf:gnstxx:v:21:y:2009:i:7:p:851-861
    DOI: 10.1080/10485250902980568
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    References listed on IDEAS

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    1. Wang, Hansheng & Xia, Yingcun, 2008. "Sliced Regression for Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 811-821, June.
    2. 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.
    3. 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.
    4. Zhu, Li-Xing & Ohtaki, Megu & Li, Yingxing, 2007. "On hybrid methods of inverse regression-based algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2621-2635, February.
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