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Nonparametric spectral-based estimation of latent structures

Authors: St├ęphane Bonhomme , Koen Jochmans and Jean-Marc Robin
Date: 01 April 2014
Type: cemmap Working Paper, CWP18/14
DOI: 10.1920/wp.cem.2014.1814

Abstract

We present a constructive identification proof of p-linear decompositions of q-way arrays. The analysis is based on the joint spectral decomposition of a set of matrices. It has applications in the analysis of a variety of latent-structure models, such as q-variate mixtures of p distributions. As such, our results provide a constructive alternative to Allman, Matias and Rhodes [2009]. The identification argument suggests a joint approximate-diagonalization estimator that is easy to implement and whose asymptotic properties we derive. We illustrate the usefulness of our approach by applying it to nonparametrically estimate multivariate finite-mixture models and hidden Markov models.

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