| Summary: | A broad class of error distributions for generalized linear models is provided by
the class of dispersion models which was introduced by Jorgensen (1987a, 1997a)
and a detailed study on dispersion models was made by Jorgensen (1997b). In this
thesis we study multivariate proper dispersion models. Our aim is to do multivariate
analysis for non-normal data, particularly data from the multivariate gamma distribution
which is an example of a multivariate proper dispersion model, introduced by
Jorgensen and Lauritzen (1998). This class provides a multivariate extension of the
dispersion model density, following the spirit of the multivariate normal density.
We consider the saddlepoint approximation for small dispersion matrices, which, in
turn, implies that the multivariate proper dispersion model is approximately multivariate
normal for small dispersion matrices.
We want to mimic the basic technique of testing in multivariate normal, Hotelling's
T². Our version of the T² test applies asymptotically, for either small dispersion or
large samples.
We also consider estimating the normalizing constant of the bivariate gamma by
Monte Carlo simulation and we investigate the marginal density by using numerical
integration. We also investigate the distribution of the T²-statistic by Monte Carlo
simulation.
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