Optimization models and methods for maximum likelihood estimation of statistical parameters

This thesis proposes optimization models and methods for maximum likelihood estimation of statistical parameters from the point of view of mathematical programming. In particular, the clustering of Mixtures of Gaussians and the Clusterwise Linear Regression problems are studied. For what concerns the first problem, a new model is proposed and an algorithm based on it is shown to perform well in practice as an heuristic. Regarding Clusterwise Linear Regression, a new probabilistic branch-and-bound algorithm is proposed that achieves competitive performance in practice as a heuristic.