Minimum information dependence modeling

We propose a method of constructing a joint statistical model for mixed-domain data to analyze their dependence. Multivariate Gaussian and log-linear models are particular examples of the proposed model. It is shown that the functional equation defining the model has a unique solution under fairly weak conditions. The model is characterized by two orthogonal sets of parameters: the dependence parameter and the marginal parameter. To estimate the dependence parameter, a conditional inference together with a sampling procedure is established and is shown to provide a consistent estimator of the dependence parameter. Illustrative examples of data analyses involving penguins and earthquakes are presented.