Maximum likelihood estimation for a bivariate Gaussian process under fixed domain asymptotics

Velandia Daira (1) , François Bachoc (2, 3) , Bevilacqua Moreno (1) , Gendre Xavier (2) , Jean-Michel Loubes (2)

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

We consider maximum likelihood estimation with data from a bivariate Gaussian process with a separable exponential covariance model under fixed domain asymptotic. We first characterize the equivalence of Gaussian measures under this model. Then consistency and asymptotic distribution for the microergodic parameters are established. A simulation study is presented in order to compare the finite sample behavior of the maximum likelihood estimator with the given asymptotic distribution.

Mots clés: Bivariate exponential model; equivalent Gaussian measures; infill asymptotics; microergodic parameters

Domaines: Statistiques [math.ST]

Velandia Daira, François Bachoc, Bevilacqua Moreno, Gendre Xavier, Jean-Michel Loubes. Maximum likelihood estimation for a bivariate Gaussian process under fixed domain asymptotics. 2016. ⟨hal-01294547⟩