Estimation of Variance Components for a Linear Toeplitz Model

The linear Toeplitz covariance structure model of order one is considered. We give some elegant explicit expressions of the Locally Minimum Variance Quadratic Unbiased Estimators of its covariance parameters. We deduce from a Monte Carlo method some properties of their Gaussian maximum likelihood estimators. Finally, for small sample sizes, these two types of estimators are compared with the intuitive empirical estimators and it is shown that the empirical biased estimators should be used.