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An analysis of single-index model with monotonic link function

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Abstract

The single-index model with monotonic link function is investigated. Firstly, it is showed that the link function h(·) can be viewed by a graphic method. That is, the plot with the fitted response ŷ on the horizontal axis and the observed y on the vertical axis can be used to visualize the link function. It is pointed out that this graphic approach is also applicable even when the link function is not monotonic. Note that many existing nonparametric smoothers can also be used to assess h(·). Therefore, the I-spline approximation of the link function via maximizing the covariance function with a penalty function is investigated in the present work. The consistency of the criterion is constructed. A small simulation is carried out to evidence the efficiency of the approach proposed in the paper.

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Authors and Affiliations

  1. School of Finance and Statist., East China Normal Univ., Shanghai, 200241, China

    Li-ping Zhu, Xiao-yan Yang & Zhou Yu

  2. Dept. of Statist., Zhejiang Univ. of Finance and Economics, Hangzhou, 310018, China

    Xiang-rong Liu

Authors
  1. Li-ping Zhu
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  2. Xiao-yan Yang
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  3. Zhou Yu
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  4. Xiang-rong Liu
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Additional information

Supported by the National Natural Science Foundation of China (10701035), ChenGuang Project of Shanghai Education Development Foundation (2007CG33), and a Special Fund for Young Teachers in Shanghai Universities (79001320).

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Zhu, Lp., Yang, Xy., Yu, Z. et al. An analysis of single-index model with monotonic link function. Appl. Math. J. Chin. Univ. 23, 107–112 (2008). https://doi.org/10.1007/s11766-008-0115-2

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  • DOI: https://doi.org/10.1007/s11766-008-0115-2

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