Estimating multivariate latent-structure models
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Authors
Bonhomme, S
Jochmans, K
Robin, JM
Publication Date
2016Journal Title
Annals of Statistics
ISSN
0090-5364
Publisher
Institute of Mathematical Statistics
Volume
44
Issue
2
Pages
540-563
Type
Article
This Version
VoR
Metadata
Show full item recordCitation
Bonhomme, S., Jochmans, K., & Robin, J. (2016). Estimating multivariate latent-structure models. Annals of Statistics, 44 (2), 540-563. https://doi.org/10.1214/15-AOS1376
Abstract
© Institute of Mathematical Statistics, 2016. 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.
Keywords
Finite mixture model, hidden Markov model, latent structure, multilinear restrictions, multivariate data, nonparametric estimation, simultaneous matrix diagonalization
Sponsorship
Supported by European Research Council Grant ERC-2010-StG-0263107-ENMUH.
Supported by Sciences Po’s SAB grant “Nonparametric estimation of finite mixtures.”
Supported by European Research Council Grant ERC-2010-AdG-269693-WASP and by Economic and Social Research Council Grant RES-589-28-0001 through the Centre for Microdata Methods and Practice.
Identifiers
External DOI: https://doi.org/10.1214/15-AOS1376
This record's URL: https://www.repository.cam.ac.uk/handle/1810/286881
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