Estimating multivariate latent-structure models
Stéphane Bonhomme, Koen Jochmans, Jean-Marc Robin
The Annals of Statistics · 2016 · Volume 44 · Issue 2
Abstract
A constructive proof of identification of multilinear decompositions of multiway arrays is presented. It can be applied to show identification in a variety of multivariate latent structures. Examples are finite-mixture models and hidden Markov models. The key step to show identification is the joint diagonalization of a set of matrices in the same nonorthogonal basis. An estimator of the latent-structure model may then be based on a sample version of this joint-diagonalization problem. Algorithms are available for computation and we derive distribution theory. We further develop asymptotic theory for orthogonal-series estimators of component densities in mixture models and emission densities in hidden Markov models.
Keywords
15A18, 15A23, 15A69, 62G05, 62G20, 62H17, 62H30, Finite mixture model, Hidden Markov model, latent structure, multilinear restrictions, multivariate data, nonparametric estimation, simultaneous matrix diagonalization
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