Minimum information dependence modeling

We propose a method of dependence modeling for a broad class of multivariate data. Multivariate Gaussian and log-linear models are particular examples of the proposed class. The proposed class is characterized by two orthogonal sets of parameters: the dependence parameters and those of marginal distributions. It is shown that the functional equation defining the model has a unique solution under fairly weak conditions. To estimate the dependence parameters, a conditional inference together with a sampling procedure is established and is shown to be asymptotically indistinguishable from maximum likelihood inference. Illustrative examples of data analyses involving penguins and earthquakes are presented.