2021/01/11 by Xavier Emery, Emery, Xavier, Emilio Porcu +4
Computer Science · Economics, Econometrics and Finance · Environmental Science · #FOS: Computer and information sciences #FOS: Mathematics #Geochemistry and Geologic Mapping #Methodology (stat.ME) #Soil Geostatistics and Mapping #Spatial and Panel Data Analysis #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2101.04235
openalex publication_date 2021/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper addresses the problem of finding parametric constraints that\nensure the validity of the multivariate Mat 'ern covariance for modeling the\nspatial correlation structure of coregionalized variables defined in an\nEuclidean space. To date, much attention has been given to the bivariate\nsetting, while the multivariate setting has been explored to a limited extent\nonly. The existing conditions often imply severe restrictions on the upper\nbounds for the collocated correlation coefficients, which makes the\nmultivariate Mat 'ern model appealing for the case of weak spatial\ncross-dependence only. We provide a collection of sufficient validity\nconditions for the multivariate Mat 'ern covariance that allows for more\nflexible parameterizations than those currently available, and prove that one\ncan attain considerably higher upper bounds for the collocated correlation\ncoefficients in comparison with our competitors. We conclude with an\nillustration on a trivariate geochemical data set and show that our enlarged\nparametric space yields better fitting performances.\n