The Annals of Statistics

Estimating multivariate latent-structure models

Stéphane Bonhomme, Koen Jochmans, and Jean-Marc Robin

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 44, Number 2 (2016), 540-563.

Dates
Received: May 2015
Revised: August 2015
First available in Project Euclid: 17 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.aos/1458245727

Digital Object Identifier
doi:10.1214/15-AOS1376

Mathematical Reviews number (MathSciNet)
MR3476609

Zentralblatt MATH identifier
1381.62055

Subjects
Primary: 15A69: Multilinear algebra, tensor products 62G05: Estimation
Secondary: 15A18: Eigenvalues, singular values, and eigenvectors 15A23: Factorization of matrices 62G20: Asymptotic properties 62H17: Contingency tables 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]

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

Citation

Bonhomme, Stéphane; Jochmans, Koen; Robin, Jean-Marc. Estimating multivariate latent-structure models. Ann. Statist. 44 (2016), no. 2, 540--563. doi:10.1214/15-AOS1376. https://projecteuclid.org/euclid.aos/1458245727


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Supplemental materials

  • Supplement to “Estimating multivariate latent-structure models”. The supplement to this paper [Bonhomme, Jochmans and Robin (2015)] contains additional details and discussion, omitted proofs and additional simulation results.