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, a restrictive lower bound on Kendall's tau, and vanishingly small likelihood gradients, making MLE brittle and limiting MoM's applicability to datasets with sufficiently strong dependence (i.e., only when the empirical Kendall's $τ$ exceeds the family's lower bound $\approx 0.545$). We introduce \textbf{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 $θ$. IGNIS utilizes a multi-input architecture and a theory-guided output layer ($\mathrm{softplus}(z) + 1$) to automatically enforce the domain constraint $\hatθ \geq 1$. 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. To our knowledge, IGNIS is the first \emph{standalone, general-purpose} neural estimator for Archimedean copulas (not a generative model or likelihood optimizer), delivering direct, constraint-aware $\hatθ$ and readily extensible to additional families via retraining or minor output-layer adaptations.

翻译：经典估计量作为统计推断的基石，在应用于新兴的重要阿基米德Copula类别时面临难以克服的挑战。这些模型表现出病态特性，包括数值不稳定的密度函数、对Kendall's tau的严格下界约束，以及趋于零的似然梯度，导致极大似然估计（MLE）脆弱，并限制了矩估计法（MoM）仅适用于具有足够强依赖性的数据集（即仅当经验Kendall's $τ$超过该族下界$\approx 0.545$时）。我们提出\textbf{IGNIS}，一个统一的神经估计框架，通过学习从数据驱动的依赖性度量到底层Copula参数$θ$的直接、鲁棒映射，绕过了这些障碍。IGNIS采用多输入架构和理论引导的输出层（$\mathrm{softplus}(z) + 1$），自动强制执行定义域约束$\hatθ \geq 1$。在四个Copula族（Gumbel、Joe以及数值上具有挑战性的A1/A2）上进行训练和验证后，IGNIS在真实世界的金融和健康数据集上提供了准确且稳定的估计，证明了其在传统方法失效的现代复杂依赖模型中进行可靠推断的必要性。据我们所知，IGNIS是首个面向阿基米德Copula的\textit{独立、通用型}神经估计器（而非生成模型或似然优化器），能够直接输出满足约束的$\hatθ$，并且通过重新训练或对输出层的微小调整，即可轻松扩展到其他Copula族。