| Tests for nonparametric parts on partially linear single index models |
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| 作者姓名： | Ri-quan ZHANG |
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| 作者单位： | Ri-quan ZHANG Department of Statistics，East China Normal University，Shanghai 200062，China; Department of Mathematics，Shanxi Datong University，Datong 037009，China |
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| 摘 要： | Tests for nonparametric parts on partially linear single index models are considered in this paper. Based on the estimates obtained by the local linear method, the generalized likelihood ratio tests for the models are established. Under the null hypotheses the normalized tests follow asymptotically the χ2-distribution with the scale constants and the degrees of freedom being independent of the nuisance parameters, which is called the Wilks phenomenon. A simulated example is used to evaluate the performances of the testing procedures empirically.
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| 关 键 词： | local linear method partially linear single index models generalized likelihood ratio test Wilks phenomenon χ2-distribution. |
| 收稿时间： | 19 May 2006 |
| 修稿时间： | 15 August 2006 |
Tests for nonparametric parts on partially linear single index models |
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| Ri-quan ZHANG.Tests for nonparametric parts on partially linear single index models[J].Science in China(Mathematics),2007,50(3):439-449. |
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| Authors: | Ri-quan Zhang |
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| Institution: | Department of Statistics, East China Normal University, Shanghai 200062, China;Department of Mathematics, Shanxi Datong University, Datong 037009, China |
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| Abstract: | Tests for nonparametric parts on partially linear single index models are considered in this paper. Based on the estimates
obtained by the local linear method, the generalized likelihood ratio tests for the models are established. Under the null
hypotheses the normalized tests follow asymptotically the χ
2-distribution with the scale constants and the degrees of freedom being independent of the nuisance parameters, which is called
the Wilks phenomenon. A simulated example is used to evaluate the performances of the testing procedures empirically.
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| Keywords: | local linear method partially linear single index models generalized likelihood ratio test Wilks phenomenon x2-distribution |
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