On Identifiability and Consistency of The Nugget in Gaussian Spatial Process Models

Abstract Spatial process models popular in geostatistics often represent the observed data as sum of a smooth underlying and white noise. The variation noise is attributed to measurement error, or microscale variability, called ‘nugget’. We formally establish results on identifiability consistency nugget spatial based upon Gaussian within framework in-fill asymptotics, that sample size increases sampling domain bounded. Our work extends fixed asymptotics for without nugget. More specifically, we parameters Matérn covariogram their maximum likelihood estimators presence discontinuities due also present simulation studies demonstrate role identifiable quantities interpolation.