Minimum phi divergence estimator and hierarchical testing in loglinear models

In this paper we consider inference based on very general divergence measures, under assumptions of multinomial sampling and loglinear models. We define the minimum phi divergence estimator, which is seen to be a generalization of the maximum likelihood estimator. This estimator is then used in a phi divergence goodness-of-fit statistic, which is the basis of two new statistics for solving the problem of testing a nested sequence of loglinear models.