IGNIS: A Robust Neural Network Framework for Constrained Parameter Estimation in Archimedean Copulas

• URL: http://arxiv.org/abs/2505.22518v3
• Date: Mon, 28 Jul 2025 08:58:45 GMT
• Title: IGNIS: A Robust Neural Network Framework for Constrained Parameter Estimation in Archimedean Copulas
• Authors: Agnideep Aich,
• Abstract summary: We introduce IGNIS, a unified neural estimation framework for Archimedean copulas.<n> IGNIS learns a direct, robust mapping from data-driven dependency measures to the underlying copula parameter theta.<n>It delivers accurate and stable estimates for real-world financial and health datasets.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Classical estimators, the cornerstones of statistical inference, face insurmountable challenges when applied to important emerging classes of Archimedean copulas. These models exhibit pathological properties, including numerically unstable densities, non-monotonic parameter-to-dependence mappings, and vanishingly small likelihood gradients, rendering methods like Maximum Likelihood (MLE) and Method of Moments (MoM) inconsistent or computationally infeasible. We introduce IGNIS, a unified neural estimation framework that sidesteps these barriers by learning a direct, robust mapping from data-driven dependency measures to the underlying copula parameter theta. IGNIS utilizes a multi-input architecture and a theory-guided output layer (softplus(z) + 1) to automatically enforce the domain constraint theta_hat >= 1. Trained and validated on four families (Gumbel, Joe, and the numerically challenging A1/A2), IGNIS delivers accurate and stable estimates for real-world financial and health datasets, demonstrating its necessity for reliable inference in modern, complex dependence models where traditional methods fail.

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