Estimating the number of components in finite mixture models via the Group-Sort-Fuse procedure

Estimation of the number components (or order) a finite mixture model is long standing and challenging problem in statistics. We propose Group-Sort-Fuse (GSF) procedure—a new penalized likelihood approach for simultaneous estimation order mixing measure multidimensional models. Unlike methods which fit compare mixtures with varying orders using criteria involving complexity, our directly penalizes continuous function parameters. More specifically, given conservative upper bound on order, GSF groups sorts component parameters to fuse those are redundant. For wide range models, we show that consistent estimating true achieves n−1/2 convergence rate parameter up polylogarithmic factors. The implemented several univariate multivariate models R package GroupSortFuse. Its sample performance supported by thorough simulation study, its application illustrated two real data examples.