Infill asymptotics for a stochastic process model with measurement error

Huann Sheng Chen, Douglas G Simpson, Zhiliang Ying

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)141-156
Number of pages16
JournalStatistica Sinica
Issue number1
StatePublished - Jan 2000


  • 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


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