Spatial Nonparametric Regression Estimation: Non-isotropic Case

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	Spatial Nonparametric Regression Estimation: Non-isotropic Case
其他题名	Spatial Nonparametric Regression Estimation: Non-isotropic Case
	Lu Zudi 1; Chen Xing 2
	2002
发表期刊	Acta Mathematicae Applicatae Sinica
ISSN	0168-9673
卷号	18 期号:4 页码:641-656
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 are required.
其他摘要	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 are required.
关键词	bandwidth kernel estimator mixing non-isotropic spatial data spatial conditional regression weak consistency and rates
收录类别	CSCD
语种	英语
CSCD记录号	CSCD:1367037
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/53043
专题	中国科学院数学与系统科学研究院
作者单位	1.中国科学院数学与系统科学研究院 2.云南大学
推荐引用方式 GB/T 7714	Lu Zudi,Chen Xing. Spatial Nonparametric Regression Estimation: Non-isotropic Case[J]. Acta Mathematicae Applicatae Sinica,2002,18(4):641-656.
APA	Lu Zudi,&Chen Xing.(2002).Spatial Nonparametric Regression Estimation: Non-isotropic Case.Acta Mathematicae Applicatae Sinica,18(4),641-656.
MLA	Lu Zudi,et al."Spatial Nonparametric Regression Estimation: Non-isotropic Case".Acta Mathematicae Applicatae Sinica 18.4(2002):641-656.