Composite likelihood estimation for a Gaussian process under fixed domain asymptotics

François Bachoc (1, 2) , Moreno Bevilacqua (3) , Daira Velandia (4)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
3 Valparaiso University
4 Unicosta - Universidad de la Costa = University of la Costa

We study composite likelihood estimation of the covariance parameters with data from 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 , depending on the range of admissible parameter values in the likelihood optimization. On the contrary, the weighted pairwise conditional maximum likelihood estimator is always consistent. Both estimators are also asymptotically Gaussian when they are consistent, with asymptotic variance 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.

Mots clés: fixed-domain asymptotics; pairwise composite likelihood; exponential model; Gaussian processes; large data sets; microergodic parameters; consistency; asymptotic normality

Domaines: Statistiques [math.ST]

François Bachoc, Moreno Bevilacqua, Daira Velandia. Composite likelihood estimation for a Gaussian process under fixed domain asymptotics . 2018. ⟨hal-01845283v2⟩