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.
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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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