Composite likelihood estimation for a Gaussian process under fixed domain asymptotics

François Bachoc, Moreno Bevilacqua, DAIRA LUZ VELANDIA MUÑOZ

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2 Scopus citations

Abstract

We study the problem of estimating the covariance parameters of a one-dimensional Gaussian process with exponential covariance function under fixed-domain asymptotics. We show that the weighted pairwise maximum likelihood estimator of the microergodic parameter can be consistent or inconsistent. This depends on the range of admissible parameter values in the likelihood optimization. On the other hand, the weighted pairwise conditional maximum likelihood estimator is always consistent. Both estimators are also asymptotically Gaussian when they are consistent. Their asymptotic variances are larger or strictly larger than that of the maximum likelihood estimator. A simulation study is presented in order to compare the finite sample behavior of the pairwise likelihood estimators with their asymptotic distributions. For more general covariance functions, an additional inconsistency result is provided, for the weighted pairwise maximum likelihood estimator of a variance parameter.

Original languageEnglish
Article number104534
JournalJournal of Multivariate Analysis
Volume174
DOIs
StatePublished - 1 Nov 2019

Keywords

  • Asymptotic normality
  • Consistency
  • Exponential model
  • Fixed-domain asymptotics
  • Gaussian processes
  • Large data sets
  • Microergodic parameters
  • Pairwise composite likelihood

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