2016/02/09 by François Bachoc, Reinhard Furrer, Bachoc, François +1
Economics, Econometrics and Finance · Environmental Science · Mathematics · #FOS: Mathematics #Soil Geostatistics and Mapping #Spatial and Panel Data Analysis #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1602.02882
openalex publication_date 2016/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There has been a growing interest in providing models for multivariate\nspatial processes. A majority of these models specify a parametric matrix\ncovariance function. Based on observations, the parameters are estimated by\nmaximum likelihood or variants thereof. While the asymptotic properties of\nmaximum likelihood estimators for univariate spatial processes have been\nanalyzed in detail, maximum likelihood estimators for multivariate spatial\nprocesses have not received their deserved attention yet. In this article we\nconsider the classical increasing-domain asymptotic setting restricting the\nminimum distance between the locations. Then, one of the main components to be\nstudied from a theoretical point of view is the asymptotic positive\ndefiniteness of the underlying covariance matrix. Based on very weak\nassumptions on the matrix covariance function we show that the smallest\neigenvalue of the covariance matrix is asymptotically bounded away from zero.\nSeveral practical implications are discussed as well.\n