## The Annals of Statistics

### Estimating multivariate latent-structure models

#### 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
Revised: August 2015
First available in Project Euclid: 17 March 2016

https://projecteuclid.org/euclid.aos/1458245727

Digital Object Identifier
doi:10.1214/15-AOS1376

Mathematical Reviews number (MathSciNet)
MR3476609

Zentralblatt MATH identifier
1381.62055

#### 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.