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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 non-orthogonal 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.
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Stéphane Bonhomme, Koen Jochmans, Jean-Marc Robin. Estimating Multivariate Latent-Structure Models. Annals of Statistics, Institute of Mathematical Statistics, 2016, 44 (2), pp.540 - 563. ⟨10.1214/15-AOS1376⟩. ⟨hal-03392022⟩

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