| Spatial Nonparametric Regression Estimation: Non-isotropic Case |
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| 作者姓名： | Zu-di Lu Xing ChenInstitute of Systems Science Academy of Mathematics and Systems Sciences Chinese Academy of Sciences. Beijing China |
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| 作者单位： | Zu-di Lu，Xing ChenInstitute of Systems Science，Academy of Mathematics and Systems Sciences，Chinese Academy of Sciences. Beijing 100080，ChinaDepartment of Statistics，Yunnan University，Kunming 650091，China |
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| 基金项目： | the National Natural Science Foundation of China (198010:38)，National 863 Project. |
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| 摘 要： | Data collected on the surface of the earth often has spatial interaction. In this paper, a non-isotropic mixing spatial data process is introduced, and under such a spatial structure a nonparametric kernel method is suggested to estimate a spatial conditional regression. Under mild regularities, sufficient conditions are derived to ensure the weak consistency as well as the convergence rates for the kernel estimator. Of interest are the following: (1) All the conditions imposed on the mixing coefficient and the bandwidth are simple; (2) Differently from the time series setting, the bandwidth is found to be dependent on the dimension of the site in space as well; (3) For weak consistency, the mixing coefficient is allowed to be unsummable and the tendency of sample size to infinity may be in different manners along different direction in space; (4) However, to have an optimal convergence rate, faster decreasing rates of mixing coefficient and the tendency of sample size to infinity along each direction a
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Spatial Nonparametric Regression Estimation: Non-isotropic Case |
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| Zu-di Lu,Xing ChenInstitute of Systems Science,Academy of Mathematics and Systems Sciences,Chinese Academy of Sciences. Beijing ,China.Spatial Nonparametric Regression Estimation: Non-isotropic Case[J].Acta Mathematicae Applicatae Sinica,2002,18(4):641-656. |
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| Authors: | Zu-di Lu Xing Chen |
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| Institution: | (1) Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China (E-mail: zdlu@amss.ac.cn), CN;(2) Department of Statistics, Yunnan University, Kunming 650091, China, CN |
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| Abstract: | Data collected on the surface of the earth often has spatial interaction. In this paper, a non-isotropic mixing spatial data process is introduced, and under such a spatial structure a nonparametric kernel method is suggested to estimate a spatial conditional regression. Under mild regularities, sufficient conditions are derived to ensure the weak consistency as well as the convergence rates for the kernel estimator. Of interest are the following: (1) All the conditions imposed on the mixing coefficient and the bandwidth are simple; (2) Differently from the time series setting, the bandwidth is found to be dependent on the dimension of the site in space as well; (3) For weak consistency, the mixing coefficient is allowed to be unsummable and the tendency of sample size to infinity may be in different manners along different direction in space; (4) However, to have an optimal convergence rate, faster decreasing rates of mixing coefficient and the tendency of sample size to infinity along each direction are required. |
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| Keywords: | Bandwidth kernel estimator mixing non-isotropic spatial data spatial conditional regression weak consistency and rates |
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