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 language | English |
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Pages (from-to) | 775-783 |
Number of pages | 9 |
Journal | Annals of the Institute of Statistical Mathematics |
Volume | 62 |
Issue number | 4 |
DOIs | |
State | Published - Aug 2010 |
Externally published | Yes |
Keywords
- Algebraic statistics
- Graphical model
- Latent variables
- Multivariate normal distribution