Open Access
April 2016 Estimating multivariate latent-structure models
Stéphane Bonhomme, Koen Jochmans, Jean-Marc Robin
Ann. Statist. 44(2): 540-563 (April 2016). DOI: 10.1214/15-AOS1376


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.


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Stéphane Bonhomme. Koen Jochmans. Jean-Marc Robin. "Estimating multivariate latent-structure models." Ann. Statist. 44 (2) 540 - 563, April 2016.


Received: 1 May 2015; Revised: 1 August 2015; Published: April 2016
First available in Project Euclid: 17 March 2016

zbMATH: 1381.62055
MathSciNet: MR3476609
Digital Object Identifier: 10.1214/15-AOS1376

Primary: 15A69 , 62G05
Secondary: 15A18‎ , 15A23 , 62G20 , 62H17 , 62H30

Keywords: Finite mixture model , Hidden Markov model , latent structure , multilinear restrictions , multivariate data , nonparametric estimation , simultaneous matrix diagonalization

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.44 • No. 2 • April 2016
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