Estimating Multivariate Latent-Structure Models

Stéphane Bonhomme (1) , Koen Jochmans (2) , Jean-Marc Robin (2, 3)

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

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.

Keywords: Estimators; Markov models; Diagonal arguments

Domains: Humanities and Social Sciences; Economics and Finance

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