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

TL;DR

This paper analyzes maximum likelihood estimation for a bivariate Gaussian process with a separable exponential covariance under fixed domain asymptotics, establishing measure equivalence, consistency, and asymptotic distribution of parameters, supported by simulation results.

Contribution

It characterizes measure equivalence and provides the first asymptotic distribution results for microergodic parameters in this setting.

Findings

MLE is consistent for microergodic parameters

Asymptotic normality of estimators is established

Simulation confirms finite sample performance aligns with asymptotic theory

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.