UCLA

Statistical modeling for massive spatial data sets has generated a substantial literature on scalable spatial processes based upon Vecchias approximation. Vecchias approximation for Gaussian process models enables fast evaluation of the likelihood by restricting dependencies at a location to its neighbors. We establish inferential properties of microergodic spatial covariance parameters within the paradigm of fixed-domain asymptotics when they are estimated using Vecchias approximation. The conditions required to formally establish these properties are explored, theoretically and empirically, and the effectiveness of Vecchias approximation is further corroborated from the standpoint of fixed-domain asymptotics.