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.
Authors
Research Fellow Sciences Po and University College London
Jean-Marc is a Research Fellow of the IFS and a Professor of Economics at Sciences Po, Paris, and University College London.
University of Cambridge
Professor of Economics University of Chicago
Working Paper details
- DOI
- 10.1920/wp.cem.2014.1814
- Publisher
- Institute for Fiscal Studies
Suggested citation
S, Bonhomme and K, Jochmans and J, Robin. (2014). Nonparametric spectral-based estimation of latent structures. London: Institute for Fiscal Studies. Available at: https://ifs.org.uk/publications/nonparametric-spectral-based-estimation-latent-structures (accessed: 2 May 2024).
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