发表机构
Acuity, A Mutual Insurance Company（Acuity，一家相互保险公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种整合复合发生-严重度建模等技术的半连续数据一致框架，解决分布不匹配问题，支持高效估计与机器学习实现，为相关应用提供统计一致的解决方案。
AI 中文摘要
半连续结果常呈现严重的分布不匹配，特征为结构零、高度偏态的正观测值及极右尾。实践中，变换、封顶、截断与删失常被用于降低极端观测值的影响，但估计程序往往仍将修正后的响应视为精确观测值，导致数据所含信息与优化的似然之间存在不匹配。本文提出一种针对半连续长尾数据的一致框架，在统一的基于似然的结构中整合复合发生-严重度建模、幂变换及右删失似然估计。该框架通过分别处理结构零质量、经验偏度及极端尾边界行为，分离分布不匹配的潜在原因，同时保留发生概率与条件严重度之间的复合关系。本文推导了闭式偏差、梯度向量及海森矩阵，支持高效的基于似然的估计及机器学习实现。所提方法为变换与删失被常规采用的应用场景中，修正半连续结果的分布不匹配提供了统计一致的方法。
英文摘要
Semicontinuous outcomes characterized by an exact zero mass and heavy-tailed continuous distributions challenge empirical risk modeling and machine learning. Compound Poisson-Gamma Tweedie processes impose a rigid mean-variance coupling that distorts zero-mass probabilities under extreme tail dispersion, flattening continuous density and reducing extreme-risk discrimination. Furthermore, heuristic post-hoc target capping introduces systematic bias while leaving loss gradients vulnerable to tail leverage. We present a unified, statistically coherent likelihood framework for semicontinuous modeling under arbitrary zero-inflation and explicit upper boundary constraints. Optimization and likelihood evaluations operate strictly in a latent space defined by the power-scaling mapping $y_i^* = \min\{(y_i/s)^λ, U^*\}$, where $s \in (0, U)$ anchors scale and $λ\in (0,1)$ regularizes tail curvature. The architecture partitions the response into three regimes: an unconstrained Bernoulli hurdle, an analytical continuous Gamma body, and an upper boundary point mass governed by incomplete Gamma survival ratios. Rather than an arbitrary truncation, the boundary functions as an intrinsic tail accumulator bounding score and Hessian dynamics. We derive the closed-form deviance objective, score vectors, and block-diagonal Hessian matrix, proving that parameter spaces are information-orthogonal to enable concurrent classification and regression updates. Asymptotic boundary analysis demonstrates that score and curvature scale linearly in the deep tail, establishing a quadratic restoring force that prevents gradient collapse. The framework breaks the Tweedie parameter rigidity paradox while maintaining structural fidelity across both zero occurrence and extreme severity differentiation.
Comments16 pages, 1 figure. v2: Revised title, expanded theoretical framework, and updated boundary derivations
