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

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

1 Unicosta - Universidad de la Costa = University of la Costa
2 Universidad de Valparaiso [Chile]
3 IMT - Institut de Mathématiques de Toulouse UMR5219

We consider maximum likelihood estimation with data from a bivariate Gaussian process with a separable exponential covariance model under fixed domain asymptotics. We first characterize the equivalence of Gaussian measures under this model. Then consistency and asymptotic normality for the maximum likelihood estimator of 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]

Daira Velandia, Moreno Bevilacqua, François Bachoc, Xavier Gendre, Jean-Michel Loubes. Maximum likelihood estimation for a bivariate Gaussian process under fixed domain asymptotics. Electronic Journal of Statistics , 2017, 11 (2), pp.2978-3007. ⟨10.1214/17-EJS1298⟩. ⟨hal-01597076⟩