title: Maximum Pseudolikelihood Estimation for Model-Based Clustering of Time Series Data.
abstract: Mixture of autoregressions (MoAR) models provide a model-based approach to the clustering of time series data. The maximum likelihood (ML) estimation of MoAR models requires evaluating products of large numbers of densities of normal random variables. In practical scenarios, these products converge to zero as the length of the time series increases, and thus the ML estimation of MoAR models becomes infeasible without the use of numerical tricks. We propose a maximum pseudolikelihood (MPL) estimation approach as an alternative to the use of numerical tricks. The MPL estimator is proved to be consistent and can be computed with an EM (expectation-maximization) algorithm. Simulations are used to assess the performance of the MPL estimator against that of the ML estimator in cases where the latter was able to be calculated. An application to the clustering of time series data arising from a resting state fMRI experiment is presented as a demonstration of the methodology.
authors.affiliation: Department of Mathematics and Statistics, La Trobe University, Victoria, Bundoora 3086, Australia hien1988@gmail.com.
authors.forename: Hien D
authors.initials: HD
authors.lastname: Nguyen
authors.affiliation: School of Mathematics and Physics, University of Queensland, St. Lucia 4072, Australia g.mclachlan@uq.edu.au.
authors.forename: Geoffrey J
authors.initials: GJ
authors.lastname: McLachlan
authors.affiliation: Centre de Recherche, Institut Universitaire de Geriatrie, Montreal H3W 1W5, Quebec, Canada pierre.orban@criugm.qc.ca.
authors.forename: Pierre
authors.initials: P
authors.lastname: Orban
authors.affiliation: Centre de Recherche, Institut Universitaire de Geriatrie, Montreal H3W 1W5, Quebec, Canada pierre.bellec@criugm.qc.ca.
authors.forename: Pierre
authors.initials: P
authors.lastname: Bellec
authors.affiliation: Centre for Advanced Imaging, University of Queensland, St. Lucia 4072, Australia andrew.janke@cai.uq.edu.au.
authors.forename: Andrew L
authors.initials: AL
authors.lastname: Janke