Performance of the maximum likelihood estimators for the parameters of multivariate generalized Gaussian distributions

This paper studies the performance of the maximum likelihood estimators (MLE) for the parameters of multivariate generalized Gaussian distributions. When the shape parameter belongs to ]0, 1[, we have proved that the scatter matrix MLE exists and is unique up to a scalar factor. After providing some elements about this proof, an estimation algorithm based on a Newton-Raphson recursion is investigated. Some experiments illustrate the convergence speed of this algorithm. The bias and consistency of the scatter matrix estimator are then studied for different values of the shape parameter. The performance of the shape parameter estimator is finally addressed by comparing its variance to the Cramér-Rao bound.