Using mixtures in seemingly unrelated linear regression models with non-normal errors

Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian distributions. Identifiability conditions are provided. The score vector and the Hessian matrix are derived. Parameter estimation is performed using the maximum likelihood method and an Expectation–Maximisation algorithm is developed. The usefulness of the proposed methods and a numerical evaluation of their properties are illustrated through the analysis of simulated and real datasets.