AI 中文总结
研究提出用鞍点近似进行计算和估计的统一框架，基于模型构建操作保留对MGF的访问，用户提供模型结构规范，软件自动组装相关函数并优化鞍点似然，还引入诊断方法，在R包中实现，展示了方法的范围和灵活性。
AI 中文摘要
鞍点近似仅使用相应的矩生成函数（MGF）就能为概率密度和质量函数提供高精度近似。近期其被越来越多地应用于似然函数，实现了在精确似然难以处理的模型中的基于似然的推断。但现有实现大多逐模型开发，因MGF的概念和计算挑战，该方法未得到充分利用。我们引入了一个使用鞍点近似进行模型构建和计算的统一框架。它基于一组模型构建操作，在允许从简单组件构建复杂分布的同时保留对MGF的访问。用户只需提供模型结构的高级规范，软件就能自动组装必要的生成函数、鞍点和梯度，并进行鞍点似然的优化。我们还引入了一种诊断方法，即使在精确似然不可用时也能量化鞍点和精确似然估计之间的差异。该框架在R包saddlepoint中实现，能快速、方便地计算参数估计、标准误差和差异诊断。众多示例说明了该方法的范围和灵活性。
英文摘要
The saddlepoint approximation provides highly accurate approximations to probability density and mass functions using only the corresponding moment generating functions (MGFs). Recent work has increasingly seen the saddlepoint approximation applied to likelihood functions, enabling likelihood-based inference in models where exact likelihoods are intractable. However, existing implementations have largely been developed on a model-by-model basis, and the methodology remains underutilized because of the conceptual and computational challenges of working with MGFs. We introduce a unified framework for model construction and computation using the saddlepoint approximation. The framework is based on a collection of model-building operations that preserve access to MGFs while allowing complex distributions to be constructed from simpler components. With these components, users need only provide a high-level specification of the model structure, from which the software automatically assembles the necessary generating functions, saddlepoints, and gradients, and performs the optimization of the saddlepoint likelihood. We also introduce a diagnostic that quantifies the difference between saddlepoint and exact likelihood estimates, even when the exact likelihood is unavailable. The framework is implemented in the R package saddlepoint and provides fast, convenient computation of parameter estimates, standard errors, and the discrepancy diagnostic. Numerous examples illustrate the scope and flexibility of the approach.
Comments41 pages, 3 figures; includes supplementary material
