Nonparametric kernel estimation of an isotropic variogram |
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| Institution: | 1. Departamento de Estatı́stica e Investigación Operativa, Facultade de Ciencias Sociais, Campus A Xunqueira, Universidade de Vigo, C.P. 36005, Pontevedra, Spain;2. Departamento de Estatı́stica e Investigación Operativa, Facultade de Matemáticas, Campus Sur, Universidade de Santiago, C.P. 15771, Santiago de Compostela, Spain;1. Center for Applied Statistics, Data Mining Center, School of Statistics, Renmin University of China, Beijing, 100872, China;2. Department of Management Sciences, Tippie College of Business, the University of Iowa, IA, 52242, USA;3. Center of Data Science and Information Quality, School of Management, Xi’an Jiaotong University, Xi’an, 710049, China;1. Department of Mathematics, University Jaume I of Castellón, Spain;2. Department of Statistics, Mathematical Analysis and Optimization, University of Santiago de Compostela, Spain;3. Department of Mathematics and Applications, University of Minho, Portugal;4. Department of Statistics and O.R., University of Valencia, Spain;1. Plant Biology and Ecology Department, University of the Basque Country UPV/EHU, Spain;2. Centre for Environmental Management (CEM), School of Geography, University of Nottingham, United Kingdom;3. UCD Centre for Veterinary Epidemiology and Risk Analysis, UCD School of Veterinary Medicine, University College Dublin, Ireland;4. Environment Department, County Council of Biscay, Spain |
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| Abstract: | In this paper, we propose nonparametric kernel estimators of the semivariogram, under the assumption of isotropy. At first, a symmetric kernel is considered in order to construct a consistent estimator, so that the selection of the bandwidth parameter is treated via the MSE or the MISE criteria. Next, the use of a boundary kernel will be suggested in order to obtain satisfactory estimates near the semivariogram endpoint. In all cases, an adaptation of Shapiro and Botha's fit is proposed to produce valid semivariogram estimators. Finally, we describe a numerical study carried out to illustrate the performance of the kernel estimators. |
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