Abstract
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.
Highlights
Gaussian processes are widely used in statistics to model spatial data
The maximum likelihood estimator (MLE) of the covariance parameters of a Gaussian stochastic process observed in Rd, d ≥ 1, has been deeply studied in the last years in the two following asymptotic frameworks
In the proof of Lemma 3, we provide asymptotic approximations and central limit theorems for terms involving the interaction of the two correlated Gaussian processes, which is a novelty compared to the univariate case
Summary
Gaussian processes are widely used in statistics to model spatial data. When fitting a Gaussian field, one has to deal with the issue of the estimation of its covariance. When d > 1 and for a separable exponential covariance function, all the covariance parameters are microergodic, and the asymptotic normality of the MLE is proved in [34] Other results in this case are given in [30, 1, 6]. Under increasing-domain asymptotics [5] extend the results of [22] to the bivariate case and consider the asymptotic distribution of the MLE for a large class of bivariate covariance models in order to test the independence between two Gaussian processes. In [18], the fixed domain asymptotic results of [34] are extended to the multivariate case, for d = 3 and when the correlation parameters between the different Gaussian processes are known. The final section provides a discussion and open problems for future research
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
