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Estimation of inverse mean: An orthogonal series approach

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  • Wang, Qin
  • Yin, Xiangrong
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    Abstract

    In this article, we propose the use of orthogonal series to estimate the inverse mean space. Compared to the original slicing scheme, it significantly improves the estimation accuracy without losing computation efficiency, especially for the heteroscedastic models. Compared to the local smoothing approach, it is more computationally efficient. The new approach also has the advantage of robustness in selecting the tuning parameter. Permutation test is used to determine the structural dimension. Moreover, a variable selection procedure is incorporated into this new approach, which is particularly useful when the model is sparse. The efficacy of the proposed method is demonstrated through simulations and a real data analysis.

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    File URL: http://www.sciencedirect.com/science/article/B6V8V-51BYS56-1/2/6a3787f3508cf8bff185f8337629ad16
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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 55 (2011)
    Issue (Month): 4 (April)
    Pages: 1656-1664

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    Handle: RePEc:eee:csdana:v:55:y:2011:i:4:p:1656-1664

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Sufficient dimension reduction Central subspace Sliced inverse regression Orthogonal series;

    References

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    1. Efstathia Bura & R. Dennis Cook, 2001. "Estimating the structural dimension of regressions via parametric inverse regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 393-410.
    2. Zhu, Lixing & Miao, Baiqi & Peng, Heng, 2006. "On Sliced Inverse Regression With High-Dimensional Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 630-643, June.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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. 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.
    9. Amato, U. & Antoniadis, A. & De Feis, I., 2006. "Dimension reduction in functional regression with applications," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2422-2446, May.
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    Cited by:
    1. Wang, Tao & Zhu, Lixing, 2013. "Sparse sufficient dimension reduction using optimal scoring," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 223-232.
    2. Scrucca, Luca, 2011. "Model-based SIR for dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 3010-3026, November.

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