Bivariate Matérn covariances with cross-dimple for modeling coregionalized variables

Spatial Statistics - Tập 41 - Trang 100491 - 2021
A. Alegría1, X. Emery2,3, E. Porcu4
1Departamento de Matemática, Universidad Técnica Federico Santa María, Valparaíso, Chile
2Department of Mining Engineering, University of Chile, Santiago, Chile
3Advanced Mining Technology Center, University of Chile, Santiago, Chile
4Department of Mathematics, Khalifa University, Abu Dhabi, The United Arab Emirates

Tài liệu tham khảo

Abramowitz, 1972 Alegría, 2020, Cross-dimple in the cross-covariance functions of bivariate isotropic random fields on spheres, Stat, 9, 10.1002/sta4.301 Alegría, 2017, The dimple problem related to space–time modeling under the Lagrangian framework, J. Multivariate Anal., 162, 110, 10.1016/j.jmva.2017.09.001 Alegría, 2019, Covariance functions for multivariate Gaussian fields evolving temporally over planet earth, Stoch. Environ. Res. Risk Assess., 33, 1593, 10.1007/s00477-019-01707-w Apanasovich, 2010, Cross-covariance functions for multivariate random fields based on latent dimensions, Biometrika, 97, 15, 10.1093/biomet/asp078 Apanasovich, 2012, A valid Matérn class of cross-covariance functions for multivariate random fields with any number of components, J. Amer. Statist. Assoc., 107, 180, 10.1080/01621459.2011.643197 Benamghar, 2014, Factorial kriging of a geochemical dataset for heavy-metal spatial-variability characterization, Environ. Earth Sci., 71, 3161, 10.1007/s12665-013-2704-5 Bevilacqua, 2015, On the flexibility of multivariate covariance models, Statist. Sci., 30, 167, 10.1214/15-STS516 Chaudhry, 1996, Asymptotics and closed form of a generalized incomplete gamma function, J. Comput. Appl. Math., 67, 371, 10.1016/0377-0427(95)00018-6 Chaudhry, 1994, Generalized incomplete gamma functions with applications, J. Comput. Appl. Math., 55, 99, 10.1016/0377-0427(94)90187-2 Chilès, 2012 Combes, 2017, Interannual variability of the subsurface eddy field in the Southeast Pacific, J. Geophys. Res.-Oceans, 120, 2769 Cuevas, 2017, Contours and dimple for the gneiting class of space-time correlation functions, Biometrika, 104, 995, 10.1093/biomet/asx048 Daley, 2015, Classes of compactly supported covariance functions for multivariate random fields, Stoch. Environ. Res. Risk Assess., 29, 1249, 10.1007/s00477-014-0996-y Di Lorenzo, 2014, Synthesis of Pacific Ocean Climate and ecosystem dynamics, Oceanography, 26, 68, 10.5670/oceanog.2013.76 Dubrule, 1983, Cross validation of kriging in a unique neighborhood, Math. Geol., 15, 687, 10.1007/BF01033232 Edwards, 2019, A multivariate global spatio-temporal stochastic generator for climate ensembles, J. Agric. Biol. Environ. Sci, 10.1007/s13253-019-00352-8 Emery, 2016, An improved spectral turning-bands algorithm for simulating stationary vector Gaussian random fields, Stoch. Environ. Res. Risk Assess., 30, 1863, 10.1007/s00477-015-1151-0 Emery, 2006, TBSIM: A computer program for conditional simulation of three-dimensional Gaussian random fields via the turning bands method, Comput. Geosci., 32, 1615, 10.1016/j.cageo.2006.03.001 Emery, 2020 Freyssinet, 2005, Ore-forming processes related to lateritic weathering, 681 Genton, 2015, Cross-covariance functions for multivariate geostatistics, Statist. Sci., 30, 147, 10.1214/14-STS487 Gneiting, 2010, Matérn cross-covariance functions for multivariate random fields, J. Amer. Statist. Assoc., 105, 1167, 10.1198/jasa.2010.tm09420 Gradshteyn, 2007 Guartán, 2021, Regionalized classification of geochemical data with filtering of measurement noises for predictive lithological mapping, Nat. Res. Res., 10.1007/s11053-020-09779-0 Hale, 2000 Harris, 2008, Incomplete Bessel, generalized incomplete gamma, or leaky aquifer functions, J. Comput. Appl. Math., 215, 260, 10.1016/j.cam.2007.04.008 Kanevski, 2004 Kent, 2011, The dimple in Gneiting’s spatial-temporal covariance model, Biometrika, 98, 489, 10.1093/biomet/asr006 Le Blévec, 2018, Geostatistical modelling of cyclic and rhythmic facies architectures, Math. Geosci., 50, 609, 10.1007/s11004-018-9737-y Li, 2011, An approach to modeling asymmetric multivariate spatial covariance structures, J. Multivariate Anal., 102, 1445, 10.1016/j.jmva.2011.05.010 Matérn, 1986 Matheron, 1965 Miller, 1998, On certain generalized incomplete gamma functions, J. Comput. Appl. Math., 91, 179, 10.1016/S0377-0427(98)00031-4 Moreva, 2016 Mosammam, 2015, The reverse dimple in potentially negative-value space–time covariance models, Stoch. Environ. Res. Risk Assess., 29, 599, 10.1007/s00477-014-0883-6 Nychka, 2015, A multi-resolution Gaussian process model for the analysis of large spatial datasets, J. Comput. Graph. Statist., 24, 579, 10.1080/10618600.2014.914946 Porcu, 2006, Nonseparable stationary anisotropic space–time covariance functions, Stoch. Environ. Res. Risk Assess., 21, 113, 10.1007/s00477-006-0048-3 Porcu, 2011, Characterization theorems for some classes of covariance functions associated to vector valued random fields, J. Multivariate Anal., 102, 1293, 10.1016/j.jmva.2011.04.013 Reinsel, 1981, Statistical analysis of stratospheric ozone data for the detection of trends, Atmos. Environ. (1967), 15, 1569, 10.1016/0004-6981(81)90140-2 Tolosana-Delgado, 2019, Geostatistics for compositional data: An overview, Math. Geosci., 51, 485, 10.1007/s11004-018-9769-3 Wackernagel, 2003 Zhang, 2010, Kriging and cross-validation for massive spatial data, Environmetrics, 21, 290, 10.1002/env.1023