Estimating Multivariate Latent-Structure Models

Stéphane Bonhomme (1) , Koen Jochmans (2) , Jean-Marc Robin (2)

1 University of Chicago
2 ECON - Département d'économie (Sciences Po)

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 simultaneous-diagonalization problem. Simple algorithms are available for computation. Asymptotic theory is derived for this joint approximate-diagonalization estimator.

Mots clés: hidden Markov model; finite mixture model; latent structure; multilinear restrictions; multivariate data; nonparametric estimation; simultaneous matrix diagonalization

Domaines: Economies et finances

Stéphane Bonhomme, Koen Jochmans, Jean-Marc Robin. Estimating Multivariate Latent-Structure Models. 2014. ⟨hal-01097135v2⟩