Infill asymptotics for a stochastic process model with measurement error

In spatial modeling the presence of measurement error, or "nugget", can hav e a big impact on the sample behavior of the parameter estimates. This arti cle investigates the nugget effect on maximum likelihood estimators for a o ne-dimensional spatial model: Omstein-Uhlenbeck plus additive white noise. Consistency and asymptotic distributions are obtained under infill asymptot ics, in which a compact interval is sampled over a finer and finer mesh as the sample size increases. Spatial infill asymptotics have a very different character than the increasing domain asymptotics familiar from time series analysis. A striking effect of measurement error is that MLE for the Omste in-Uhlenbeck component of the parameter vector is only fourth-root-n consis tent, whereas the MLE for the measurement error variance has the usual root -n rate.