- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- Some statistical properties of multivariate proper...
Open Collections
UBC Theses and Dissertations
UBC Theses and Dissertations
Some statistical properties of multivariate proper dispersion models, with special reference to a multivariate gamma model Rajeswaran, Jeevanantham
Abstract
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.
Item Metadata
Title |
Some statistical properties of multivariate proper dispersion models, with special reference to a multivariate gamma model
|
Creator | |
Publisher |
University of British Columbia
|
Date Issued |
1998
|
Description |
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.
|
Extent |
3068259 bytes
|
Genre | |
Type | |
File Format |
application/pdf
|
Language |
eng
|
Date Available |
2009-05-26
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
|
DOI |
10.14288/1.0088555
|
URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
|
Graduation Date |
1998-11
|
Campus | |
Scholarly Level |
Graduate
|
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.