Minimum information dependence modeling

TL;DR

This paper introduces a novel joint statistical model for mixed-domain data dependence, providing a unique solution, a consistent estimator for the dependence parameter, and demonstrating its application through real-world examples.

Contribution

It develops a new dependence modeling framework for mixed-domain data with a unique solution and an effective estimation method, expanding the tools for multivariate analysis.

Findings

The model has a unique solution under weak conditions.

A consistent estimator for the dependence parameter is proposed.

Illustrative examples demonstrate practical applicability.

Abstract

We propose a method to construct 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 parameters: the dependence parameter and the marginal parameter. To estimate the dependence parameter, a conditional inference together with a sampling procedure is proposed and is shown to provide a consistent estimator. Illustrative examples of data analyses involving penguins and earthquakes are presented.