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Estimating Multivariate Latent-structure Models

Bonhomme, S; Jochmans, K; Robin, J-M; (2016) Estimating Multivariate Latent-structure Models. Annals of Statistics , 44 (2) pp. 540-563. 10.1214/15-AOS1376. Green open access

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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.

Type: Article
Title: Estimating Multivariate Latent-structure Models
Open access status: An open access version is available from UCL Discovery
DOI: 10.1214/15-AOS1376
Publisher version: http://doi.org/10.1214/15-AOS1376
Language: English
Additional information: Copyright © Institute of Mathematical Statistics, 2016. All rights reserved.
Keywords: Finite mixture model, hidden Markov model, latent structure, multilinear restrictions, multivariate data, nonparametric estimation, simultaneous matrix diagonalization
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS > Dept of Economics
URI: https://discovery.ucl.ac.uk/id/eprint/1517956
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