Asymptotic minimum discrimination information measure for asymptotically weakly stationary processes

An explicit expression is derived for the minimum discrimination information (MDI) measure with respect to Gaussian priors for sources characterized by their mean and by any principal leading block of their covariance matrix. An explicit expression is provided for the MDI extension of the given partial covariance of the source with respect to a Gaussian prior. For zero-mean sources and zero-mean Gaussian priors that are asymptotically weakly stationary (AWS) processes, it is shown that the asymptotic MDI measure equals half the Itakura-Saito distortion measure between the asymptotic power spectral densities of the source and prior. Asymptotic MDI modelling of a given AWS source by autoregressive and autoregressive moving average models, which are AWS models, is considered, and conditions are given for convergence of the sample covariance estimator of the source to the stationary covariance used in the modelling