Almost sure convergence of Titterington´s recursive estimator for mixture models

Titterington (see Journal of Royal Statistical Society, B, vol.46, p.257-67, 1984) proposed a recursive parameter estimation algorithm for finite mixture models. However, due to the well known problem of singularities and multiple maximum, minimum and saddle points that are possible on the likelihood surfaces, convergence analysis has seldom been made in the past years. In this paper, under mild conditions, we show the global convergence of Titterington´s recursive estimator and its MAP variant for mixture models of the full regular exponential family.