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On identifiability and consistency of the nugget in Gaussian spatial process models


Spatial process models popular in geostatistics often represent the observed data as the sum of a smoothunderlying process and white noise. The variation in the white noise is attributed to measurement error,or micro-scale variability, and is called the “nugget”. We formally establish results on the identifiabilityand consistency of the nugget in spatial models based upon the Gaussian process within the framework ofin-fill asymptotics, i.e. the sample size increases within a sampling domain that is bounded. Our workextends results in fixed domain asymptotics for spatial models without the nugget. More specifically, weestablish the identifiability of parameters in the Matérn covariogram and the consistency of their maximumlikelihood estimators in the presence of discontinuities due to the nugget. We also present simulationstudies to demonstrate the role of the identifiable quantities in spatial interpolation.

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