  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.
