Abstract
In spatial modeling the presence of measurement error, or "nugget", can have a big impact on the sample behavior of the parameter estimates. This article investigates the nugget effect on maximum likelihood estimators for a one-dimensional spatial model: Ornstein-Uhlenbeck plus additive white noise. Consistency and asymptotic distributions are obtained under infill asymptotics, 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 Ornstein-Uhlenbeck component of the parameter vector is only fourth-root-n consistent, whereas the MLE for the measurement error variance has the usual root-n rate.
Original language | English (US) |
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Pages (from-to) | 141-156 |
Number of pages | 16 |
Journal | Statistica Sinica |
Volume | 10 |
Issue number | 1 |
State | Published - Jan 2000 |
Keywords
- Asymptotic normality
- Consistency
- Covariance
- Gaussian process
- Identifiability
- Maximum likelihood estimator
- Measurement error
- Rate of convergence
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty