Point and interval estimation for the Flexible Dirichlet model

The Flexible Dirichlet distribution (Ongaro, A., Migliorati, S., Monti, G.S., “A new distribution on the simplex containing the Dirichlet family”, Proceedings of CODAWORK’08, The 3rd Compositional Data Analysis Workshop, University of Girona, Spain, 2008) allows to preserve many mathematical and compositional properties of the Dirichlet without inheriting its lack of flexibility in modeling the various independence concepts appropriate for compositional data. The present paper addresses some inferential aspects of the model. The attention is mainly focused on maximum likelihood estimation of the parameters. This can be handled by means of the E–M algorithm which can be suitably adapted in order to take advantage of the peculiar finite mixture structure of the model. Yet, the estimation of the (asymptotic) variance-covariance matrix of the estimators is quite a challenging issue. Various alternatives have been considered and it is shown that the most feasible and efficient relies on a bootstrap evaluation of a suitable (complete-data based) expression for the observed information matrix. A simulation study is carried out to evaluate the accuracy of the proposed procedures. An application of the model to a real da ta set highlights its potential with respect to alternative models