Estimating Multivariate Latent-Structure Models
Sciences Po Economics Discussion Papers : 2014-18
hidden Markov model, finite mixture model, latent structure, multilinear restrictions, multivariate data, nonparametric estimation, simultaneous matrix diagonalization.
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.