| An analysis of single-index model with monotonic link function |
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| 作者姓名： | ZHU Li-ping~ YANG Xiao-yan~ YU Zhou~ LIU Xiang-rong~ School of Finance and Statist. East China Normal Univ. Shanghai China. Dept.of Statist. Zhejiang Univ.of Finance and Economics Hangzhou China. |
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| 作者单位： | ZHU Li-ping~1 YANG Xiao-yan~1 YU Zhou~1 LIU Xiang-rong~2 1 School of Finance and Statist.，East China Normal Univ.，Shanghai 200241，China. 2 Dept.of Statist.，Zhejiang Univ.of Finance and Economics，Hangzhou 310018，China. |
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| 基金项目： | 国家自然科学基金，Chen Guang Project of Shang-hai Education Development Foundation，Special Fund for Young Teachers in Shanghai Universities |
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| 摘 要： | 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 y 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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| 关 键 词： | 单调 量纲 图解 图形 |
| 收稿时间： | 22 May 2007 |
An analysis of single-index model with monotonic link function |
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| ZHU Li-ping YANG Xiao-yan YU Zhou LIU Xiang-rong School of Finance and Statist.,East China Normal Univ.,Shanghai ,China. Dept.of Statist.,Zhejiang Univ.of Finance and Economics,Hangzhou ,China..An analysis of single-index model with monotonic link function[J].Applied Mathematics A Journal of Chinese Universities,2008,23(1):107-112. |
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| Authors: | Li-ping Zhu Xiao-yan Yang Zhou Yu Xiang-rong Liu |
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| Institution: | [1]School of Finance and Statist., East China Normal Univ., Shanghai 200241, China. [2]Dept. of Statist., Zhejiang Univ. of Finance and Economics, Hangzhou 310018, China. |
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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 y 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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| Keywords: | dimension reduction graphic regression I-spline monotonicity single-index model |
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