A new class of semiparametric semivariogram and nugget estimators

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• 作者：Patrick S. Carmack^a ; ^{patrickc@uca.edu} ; Jeffrey S. Spence^b ; William R. Schucany^c ; Richard F. Gunst^c ; Qihua Lin^b ; Robert W. Haley^b
• 关键词：Unsupervised brain imaging ; Nonparametric ; Bessel basis ; Isotropic ; Node space ; Regular lattice ; Negative definiteness
• 刊名：Computational Statistics and Data Analysis
• 出版年：2012
• 期刊代码：19_01679473
• 类别：cp
• 出版时间：June, 2012
• 卷：56
• 期：6
• 页码：1737-1747
• 文件大小：1381 K

摘要

Several authors have proposed nonparametric semivariogram estimators. did so by application of Bochner鈥檚 theorem and further investigated this technique where it performed favorably against parametric estimators even when data were generated under the parametric model. While the former makes allowances for a prescribed nugget and the latter outlines a possible approach, neither of these demonstrate nugget estimation in practice, which is essential to spatial modeling and proper statistical inference. We propose a modified form of this method, which admits practical nugget estimation and broadens the basis. This is achieved by a simple change to the basis and an appropriate restriction of the node space as dictated by the first root of the Bessel function of the first kind of order . The efficacy of this new unsupervised semiparametric method is demonstrated via application and simulation, where it is shown to be comparable with correctly specified parametric models while outperforming misspecified ones. We conclude with remarks about selecting the appropriate basis and node space definition.