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Media type:
E-Article
Title:
SMALL DISPERSION ASYMPTOTICS
Contributor:
Jørgensen, Bent
imprint:
Brazilian Statistical Association, 1987
Published in:Brazilian Journal of Probability and Statistics
Language:
English
ISSN:
0103-0752;
2317-6199
Origination:
Footnote:
Description:
<p>We show that, under regularity conditions, dispersion models (models in the extended class of generalized linear model of Jørgensen (1983) ) are approximately normal for large values of the index parameter. This is shown to imply that standard large sample theory applies for large values of the index parameter, as well as for large sample sizes. Thus, the log likelihood ratio test is asymptotically X²-distributed in this limit, and the maximum likelihood estimate and the score statistic are asymptotically normally distributed. More generally, the analysis of deviance for dispersion models may be modified in such a way that the asymptotic results hold for large values of the index parameter as well as for large sample sizes.</p>