Nonparametric spectral-based estimation of latent structures

Stéphane Bonhomme, Koen Jochmans and Jean-Marc Robin

No CWP18/14, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

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.

Date: 2014-04-01
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Working Paper: Nonparametric spectral-based estimation of latent structures (2014)
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