A Maximum Entropy Copula Model for Mixed Data: Representation, Estimation, and Applications

TL;DR

This paper introduces a nonparametric maximum-entropy copula model capable of handling mixed discrete and continuous data, providing valid density estimates with interpretable parameters and demonstrating practical applications.

Contribution

It develops a novel MaxEnt copula model for mixed data that guarantees valid density estimation and unifies various statistical methods.

Findings

Model effectively handles mixed data types.

Provides valid, interpretable density estimates.

Demonstrates practical applications with real data.

Abstract

A new nonparametric model of maximum-entropy (MaxEnt) copula density function is proposed, which offers the following advantages: (i) it is valid for mixed random vector. By `mixed' we mean the method works for any combination of discrete or continuous variables in a fully automated manner; (ii) it yields a bonafide density estimate with intepretable parameters. By `bonafide' we mean the estimate guarantees to be a non-negative function, integrates to 1; and (iii) it plays a unifying role in our understanding of a large class of statistical methods. Our approach utilizes modern machinery of nonparametric statistics to represent and approximate log-copula density function via LP-Fourier transform. Several real-data examples are also provided to explore the key theoretical and practical implications of the theory.