| Testing heteroscedasticity by wavelets in a nonparametric regression model |
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| 作者姓名： | IP Waicheung |
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| 作者单位： | Department of |
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| 基金项目： | 国家自然科学基金;广东省广州市教育局资助项目;广东省广州市科技局科技计划 |
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| 摘 要： | In the nonparametric regression models, a homoscedastic structure is usually assumed. However, the homoscedasticity cannot be guaranteed a priori. Hence, testing the heteroscedasticity is needed. In this paper we propose a consistent nonparametric test for heteroscedasticity, based on wavelets. The empirical wavelet coefficients of the conditional variance in a regression model are defined first. Then they are shown to be asymptotically normal, based on which a test statistic for the heteroscedasticity is constructed by using Fan's wavelet thresholding idea. Simulations show that our test is superior to the traditional nonparametric test.
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| 收稿时间： | 12 February 2004 |
| 修稿时间： | 29 May 2006 |
Testing heteroscedasticity by wavelets in a nonparametric regression model |
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| IP Waicheung.Testing heteroscedasticity by wavelets in a nonparametric regression model[J].Science in China(Mathematics),2006,49(9):1211-1222. |
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| Authors: | LI Yuan WONG Heung IP Waicheung |
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| Institution: | 1. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
2. Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China |
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| Abstract: | In the nonparametric regression models, a homoscedastic structure is usually assumed. However, the homoscedasticity cannot be guaranteed a priori. Hence, testing the heteroscedasticity is needed. In this paper we propose a consistent nonparametric test for heteroscedasticity, based on wavelets. The empirical wavelet coefficients of the conditional variance in a regression model are defined first. Then they are shown to be asymptotically normal, based on which a test statistic for the heteroscedasticity is constructed by using Fan's wavelet thresholding idea. Simulations show that our test is superior to the traditional nonparametric test. |
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| Keywords: | regression model heteroscedasticity significance test wavelets |
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