Abstract: We propose a unified approach to maximum likelihood estimation, classification, and statistical learning in the context of finite mixture models, based on observations that can be considered a collection of order statistics. We consider both supervised and unsupervised learning approaches. New missing-data mechanisms and expectation-maximization (EM) algorithms are developed to exploit the structure of the observed data in the estimation process under each learning strategy. In addition, we present model-based classification criteria, and show how they can be used to conduct better inferences about rarely observed components in finite mixture models. Using simulation studies, we evaluate the performance of the estimation and classification methodologies. Finally the proposed methods are applied to data from a fishery study to estimate the age structure of Spot, a short-lived fish species.

Key words and phrases: Classification, EM algorithm, finite mixture models, latent variables, order statistics, ranked-set sampling.