This research explores factor analysis applied to data from skewed distributions
for the general skew model, the selection-elliptical model, the selection-normal model,
the skew-elliptical model and the skew-normal model for finite sample sizes. In
terms of asymptotics, or large sample sizes, quasi-maximum likelihood methods are
broached numerically. The skewed models are formed using selection distribution
theory, which is based on Rao’s weighted distribution theory. The models assume
the observed variable of the factor model is from a skewed distribution by defining the
distribution of the unobserved common factors skewed and the unobserved unique
factors symmetric. Numerical examples are provided using maximum likelihood selection
skew-normal factor analysis. The numerical examples, such as maximum
likelihood parameter estimation with the resolution of the “sign switching” problem
and model fitting using likelihood methods, illustrate that the selection skew-normal
factor analysis model better fits skew-normal data than does the normal factor analysis
model.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/149548 |
| Date | 03 October 2013 |
| Creators | Gaucher, Beverly Jane |
| Contributors | Hart, Jeffrey, Wehrly, Thomas, Dabney, Alan, Jansen, Dennis |
| Source Sets | Texas A and M University |
| Language | English |
| Detected Language | English |
| Type | Thesis, text |
| Format | application/pdf |
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