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Estimation of inverse mean: An orthogonal series approach

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  • Wang, Qin
  • Yin, Xiangrong

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.

Suggested Citation

  • Wang, Qin & Yin, Xiangrong, 2011. "Estimation of inverse mean: An orthogonal series approach," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1656-1664, April.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:4:p:1656-1664
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    References listed on IDEAS

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    1. 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. 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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