ESTIMATING MULTIVARIATE LATENT-STRUCTURE MODELS

• 成果类型: Article
• 署名作者: Bonhomme, Stephane; Jochmans, Koen; Robin, Jean-Marc
• 署名单位: University of Chicago; Institut d'Etudes Politiques Paris (Sciences Po); University of London; University College London
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1376
• 发表日期: 2016
• 页码: 540-563
• 关键词: canonical polyadic decomposition; nonparametric identification; uniqueness; inference; diagonalization; Identifiability; distributions; algorithm; rank

摘要

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.