New estimates and tests of independence in some copula models

TL;DR

This paper develops new statistical estimates and tests for independence in copula models with unknown margins, utilizing phi-divergences and duality, with proven asymptotic properties and simulation-based efficiency-robustness insights.

Contribution

It introduces novel estimation and testing methods for copula models using phi-divergences, including asymptotic laws for various parameter boundary conditions.

Findings

Chi-squared divergence offers good efficiency-robustness balance

Asymptotic laws established for interior and boundary parameters

Simulation results confirm effectiveness of proposed methods

Abstract

We introduce new estimates and tests of independence in copula models with unknown margins using $\phi$-divergences and the duality technique. The asymptotic laws of the estimates and the test statistics are established both when the parameter is an interior or a boundary value of the parameter space. Simulation results show that the choice of $\chi^2$-divergence has good properties in terms of efficiency-robustness.