Approximate EM algorithm for sparse estimation of multivariate location-scale mixture of normal

Parameter estimation of distributions with intractable density, such as the Elliptical Stable, often involves high-dimensional integrals requiring numerical integration or approximation. This paper introduces a novel Expectation-Maximisation algorithm for fitting such models that exploits the fast Fourier integration for computing the expectation step. As a further contribution we show that by slightly modifying the objective function, the proposed algorithm also handle sparse estimation of non-Gaussian models. The method is subsequently applied to the problem of selecting the asset within a sparse non-Gaussian portfolio optimisation framework.