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Spatial Nonparametric Regression Estimation: Non-isotropic Case

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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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Authors and Affiliations

  1. Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, 100080, China

    Zu-di Lu

  2. Department of Statistics, Yunnan University, Kunming, 650091, China

    Xing Chen

Authors
  1. Zu-di Lu
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  2. Xing Chen
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Correspondence to Zu-di Lu.

Additional information

Supported by the National Natural Science Foundation of China (No. 19801038) and National 863 Project.

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Lu, Zd., Chen, X. Spatial Nonparametric Regression Estimation: Non-isotropic Case. Acta Mathematicae Applicatae Sinica, English Series 18, 641–656 (2002). https://doi.org/10.1007/s102550200067

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  • DOI: https://doi.org/10.1007/s102550200067

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