A Kernel Variogram Estimator for Clustered Data |
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Authors: | RAQUEL MENEZES,PILAR GARCIA-SOIDÁ N, MANUEL FEBRERO-BANDE |
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Affiliation: | Department of Mathematics for Science and Technology, University of Minho;Department of Statistics and Operations Research, University of Vigo;Department of Statistics and Operations Research, University of Santiago de Compostela |
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Abstract: | Abstract. The variogram provides an important method for measuring the dependence of attribute values between spatial locations. Suppose that the nature of the sampling process leads to the presence of clustered data; it would be advisable to use a variogram estimator that aims to adjust for clustering of samples. In this setting, the use of a non-parametric weighted estimator, obtained by considering an inverse weight to a given neighbourhood density combined with the kernel method, seems to have a satisfactory behaviour in practice. This paper pursues a theoretical study of the cluster robust estimator, by proving that it is asymptotically unbiased as well as consistent and by providing criteria for selection of the bandwidth parameter and the neighbourhood radius. Numerical studies are also included to illustrate the performance of the considered estimator and the suggested approaches. |
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Keywords: | cluster isotropy kernel method variogram |
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