On Bahadur asymptotic efficiency of the maximum likelihood and quasi-maximum likelihood estimators in Gaussian stationary processes (Q1613579)

A spectral parameter of a mean zero Gaussian stationary process is estimated by maximum-likelihood (ML) and quasi-maximum-likelihood (qML) methods. It is shown that under some conditions the estimators are asymptotically efficient in the sense of Bahadur. A basic result of large deviation probability of a certain quadratic form is proved and by the help of it the exponential convergence rates of tail probabilities of these estimators are obtained. Efron's statistical curvature of Gaussian stationary processes is used in order to show the identity of the exponential convergence rates of the ML and qML estimators.