| DIMENSION-REDUCTION TYPE TESTFOR LINEARITY OF ASTOCHASTIC REGRESSION MODEL |
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| 引用本文： | 朱力行,李润泽. DIMENSION-REDUCTION TYPE TESTFOR LINEARITY OF ASTOCHASTIC REGRESSION MODEL[J]. 应用数学学报(英文版), 1998, 14(2): 165-175. DOI: 10.1007/BF02677423 |
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| 作者姓名： | 朱力行 李润泽 |
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| 作者单位： | Institute of Applied Mathematics，the Chinese Academy of Sciences，Beijing 100080，China |
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| 摘 要： | 1.IntroductionLinearregressionmodelsarewidelyusedinstatisticalanalysisofexperimentalandobservationaldata,thatis,oneoftenemploysastandardlinearmodely=or K: E,a.s.,(1.1)todostatisticalanalysis,whereydenotesascalaroutcomevariableand2denotesaP-dimensionalcolumnvectorofregressorvariables.Thismodelmeansthattheprojectionofthepdimensionalexplanatory2ontotheone-dimensionalsubspaceadZcapturesalltheinformationweneedtoknowabouttheoutcomevariabley.Thisisadimension-reductionmodel.Hencewemayreachthegoalofd…
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| 收稿时间： | 1995-01-10 |
Dimension-reduction type test for linearity of a stochastic regression model |
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| Zhu Lixing,Li Runze. Dimension-reduction type test for linearity of a stochastic regression model[J]. Acta Mathematicae Applicatae Sinica, 1998, 14(2): 165-175. DOI: 10.1007/BF02677423 |
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| Authors: | Zhu Lixing Li Runze |
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| Affiliation: | (1) Institute of Applied Mathematics, the Chinese Academy of Sciences, 100080 Beijing, China |
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| Abstract: | This article investigates the test for linearity of a multivariate stochastic regression model.The use of nonparametric regression procedures for developing regression diagnostics has beenthe subject of several recent research efforts. However, when the dimension of the regressor islarge, some traditional nonparametric methods, such as kernel estimation, may be inefficient.We in this article suggest two test statistics based on projection pursuit technique and kernelmethod. The tests proposed are consistent against all fixed smooth alternatives to linearityand are asymptotically distribution-free for the distribution of the error. Furthermore, the testsare applied to an example of real-life data and some simulated data sets to demonstrate theavailability of the tests proposed. |
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| Keywords: | Kernel estimate number-theoretic method projection pursuit regression model test of linearity |
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