Title: Estimating the number of components in finite mixture models via the group-sort-fuse procedure
Authors: Tudor Manole - Carnegie Mellon University (United States)
Abbas Khalili - McGill University (Canada) [presenting]
Abstract: Estimation of the number of components (or order) of a finite mixture model is a long-standing and challenging problem in statistics. We propose the Group-Sort-Fuse (GSF) procedure, a new penalized likelihood approach for simultaneous estimation of the order and mixing measure in multidimensional finite mixture models. Unlike methods that fit and compare mixtures with varying orders using criteria involving model complexity, our approach directly penalizes a continuous function of the model parameters. More specifically, given a conservative upper bound on the order, the GSF groups and sorts mixture component parameters to fuse those which are redundant. For a wide range of finite mixture models, we show that the GSF is consistent in estimating the true mixture order. The GSF is implemented for several univariate and multivariate mixture models in the R package GroupSortFuse. Its finite sample performance is supported by a thorough simulation study, and its application is illustrated on two real data examples.