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| Testing for additivity with B-splines | |
| 作者单位： | Heng-jian CUI（Department of Statistics and Financial Mathematics, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China） ; Xu-ming HE （Department of Statistics, University of Illinois, Champaign, IL 61820, USA） ; Li LIU（National Institute of Statistical Science, Durham, NC 27709, USA） ; |
| 基金项目： | 国家自然科学基金;国家自然科学基金 |
| 摘 要： | Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey's one degree of freedom test and a nonparametric version of Rao's score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance. |
| 收稿时间： | 12 September 2005 |
| 修稿时间： | 10 January 2007 |
Testing for additivity with B-splines |
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| Authors: | Heng-jian Cui Xu-ming He Li Liu |
| Institution: | 1. Department of Statistics and Financial Mathematics, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China 2. Department of Statistics, University of Illinois, Champaign, IL 61820, USA 3. National Institute of Statistical Science, Durham, NC 27709, USA |
| Abstract: | Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey's one degree of freedom test and a nonparametric version of Rao's score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance. |
| Keywords: | additivity B-splines dimension reduction score test smoothing Tukey test |
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