B0704
Title: Nonparametric consistency for ML-based clustering with finite mixtures of elliptically symmetric distributions
Authors: Christian Hennig - University of Bologna (Italy)
Pietro Coretto - University of Salerno (Italy) [presenting]
Abstract: The $k$-means method is often referred to as nonparametric, based on the nonparametric consistency theorem, which shows that without assuming any parametric model, under general conditions, the $k$-means solution converges to its own canonical functional (population version). We prove a similar result for a constrained MLE for finite mixtures of a general class of elliptically symmetric distributions (including popular models such as the Gaussian, Student-t, and Laplace, etc.). We also show that for data generated from distributions producing ``clear clustering'', the partition implied by the value of the ML canonical functional can be interpreted appropriately as corresponding to the clusters in the population.
