Bonhomme, S. and Jochmans, K. and Robin, J-M.

Estimating Multivariate Latent-Structure Models

Annals of Statistics

Vol. 44(2) pp. 540-563 (2016)

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.

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Publisher's Link: http://dx.doi.org/10.1214/15-AOS1376