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Title: Mixed parametrization, IPF and fixed point algorithms in marginal models Authors:  Antonio Forcina - Perugia (Italy) [presenting]
Abstract: Distributions belonging to the exponential family may be parameterized by combining an arbitrary selection of mean parameters with the complementary set of canonical parameters. Within the multinomial distribution, mean parameters are marginal probabilities while canonical parameters are log-linear contrasts. A Newton algorithm may be used to reconstruct the joint distribution with a given mixed parametrization. Because any set of log-linear parameters are variation independent and the mean parameters are also variation independent from the canonical parameters, the corresponding joint distribution will always exist as long as the mean parameters are internally consistent. The reconstruction algorithm may be seen as an alternative to IPF for fitting log-linear models by setting the mean parameters to the observed marginals and the complementary set of log-linear parameters to 0 (or to arbitrary values). The same algorithm may be used to show that a collection of log-linear parameters defined within different marginal distributions are smooth when marginals may be ordered so that each one is parameterized by a set of log-linear parameters combined with the mean parameters available from preceding marginals. Arguments based on fixed point algorithms combined with the mixed parametrization have been used to prove smoothness of more complex marginal parameterizations.