FIXED-DOMAIN ASYMPTOTICS UNDER VECCHIA'S APPROXIMATION OF SPATIAL PROCESS LIKELIHOODS

Statistical modeling for massive spatial data sets has generated a substantial body of literature on scalable spatial processes based on Vecchia'sapproximation.Vecchia's approximation for Gaussian process models enablesfast evaluation of the likelihood by restricting dependencies at a location to itsneighbors. We establish inferential properties of microergodic spatial covarianceparameters within the paradigm of fixed-domain asymptotics when the parametersare estimated using Vecchia's approximation. We explore the conditions requiredto formally establish these properties, theoretically and empirically. Our resultsfurther corroborate the effectiveness of Vecchia's approximation from the standpoint of fixed-domain asymptotics