An alternative to standard maximum likelihood for Gaussian mixtures
Because true maximum likelihood (ML) is too expensive, the dominant approach in Bernoulli-Gaussian (BG) myopic deconvolution consists in the joint maximization of a single generalized likelihood with respect to the input signal and the hyperparameters. This article assesses the theoretical properties of a related maximum generalized marginal likelihood (MGML) estimator in a simplified framework: the filter is reduced to identity, so that the output data is a mixture of Gaussian populations. Our results are three-fold: first, exact MGML estimates can be efficiently computed; second, this estimator performs better than ML in the short sample case whereas it is drastically less expensive; third, asymptotic estimates are significant although biased.