Expected likelihood estimation: Asymptotic properties for "stochastic" complex Gaussian models

Expected likelihood estimation allows for the "quality assessment" of potential parameter estimates based on the likelihood ratio (LR) of the covariance matrix model constructed with parameter estimates. A solution is considered acceptable and further iterative refinement of the estimation process is terminated when the observed LR is statistically as good as the LR of the unknown true solution. We derive the asymptotic performance of expected likelihood and show it has a larger average error than the Cramer-Rao bound and is therefore not technically efficient. However, the degradation in the error is fixed, relatively small, and a function of the dimension of the data vector M, so expected likelihood can be used to impose useful statistical bounds on the likelihood function (LF) value.