Statistical models defined by imposing restrictions on marginal
distributions of contingency tables have received considerable attention
recently. This paper introduces a general definition of marginal log-linear
parameters and describes conditions for a marginal log-linear parameter to be a
smooth parameterization of the distribution and to be variation independent.
Statistical models defined by imposing affine restrictions on the marginal
log-linear parameters are investigated. These models generalize ordinary
log-linear and multivariate logistic models. Sufficient conditions for a
log-affine marginal model to be nonempty and to be a curved exponential family
are given. Standard large-sample theory is shown to apply to maximum likelihood
estimation of log-affine marginal models for a variety of sampling
procedures.
Publié le : 2002-02-14
Classification:
Marginal log-linear parameters,
log-affine and log-linear marginal models,
smooth parameterization,
variation independence,
existence and connectedness of a model,
curved exponential family,
asymptotic normality of maximum likelihood
estimates,
62H17,
62E99
@article{1015362188,
author = {Bergsma, Wicher P. and Rudas, Tam\'as},
title = {Marginal models for categorical data},
journal = {Ann. Statist.},
volume = {30},
number = {1},
year = {2002},
pages = { 140-159},
language = {en},
url = {http://dml.mathdoc.fr/item/1015362188}
}
Bergsma, Wicher P.; Rudas, Tamás. Marginal models for categorical data. Ann. Statist., Tome 30 (2002) no. 1, pp. 140-159. http://gdmltest.u-ga.fr/item/1015362188/