Finiteness of small factor analysis models

Mathias Drton, Han Xiao

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We consider factor analysis models with one or two factors. Fixing the number of factors, we prove a finiteness result about the covariance matrix parameter space when the size of the covariance matrix increases. According to this result, there exists a distinguished matrix size starting at which one can determine whether a given covariance matrix belongs to the parameter space by determining whether all principal submatrices of the distinguished size belong to the corresponding parameter space. We show that the distinguished matrix size is four in the model with one factor and six with two factors .

Original languageEnglish
Pages (from-to)775-783
Number of pages9
JournalAnnals of the Institute of Statistical Mathematics
Volume62
Issue number4
DOIs
StatePublished - Aug 2010
Externally publishedYes

Keywords

  • Algebraic statistics
  • Graphical model
  • Latent variables
  • Multivariate normal distribution

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