Asymptotic analysis for related inference problems often involves similar steps and proofs. These intermediate results could be shared across problems if each of them is made self-contained and easily identified. However, asymptotic analysis using Taylor expansions is limited for result borrowing because it is a step-to-step procedural approach. This article introduces EEsy, a modular system for estimating finite and infinitely dimensional parameters in related inference problems. It is based on the infinite-dimensional Z-estimation theorem, Donsker and Glivenko-Cantelli preservation theorems, and weight calibration techniques. This article identifies the systematic nature of these tools and consolidates them into one system containing several modules, which can be built, shared, and extended in a modular manner. This change to the structure of method development allows related methods to be developed in parallel and complex problems to be solved collaboratively, expediting the development of new analytical methods. This article considers four related inference problems -- estimating parameters with random sampling, two-phase sampling, auxiliary information incorporation, and model misspecification. We illustrate this modular approach by systematically developing 9 parameter estimators and 18 variance estimators for the four related inference problems regarding semi-parametric additive hazards models. Simulation studies show the obtained asymptotic results for these 27 estimators are valid. In the end, I describe how this system can simplify the use of empirical process theory, a powerful but challenging tool to be adopted by the broad community of methods developers. I discuss challenges and the extension of this system to other inference problems.

翻译：针对相关推断问题的渐近分析通常涉及相似的步骤和论证过程。若使每个中间结果自包含且易于识别，则可在不同问题间共享。然而，基于泰勒展开的渐近分析因其逐步程序化的特性而限制了结果复用。本文介绍了EEsy系统——一个面向相关推断问题中有限维及无限维参数估计的模块化系统。该系统建立在无限维Z估计定理、Donsker与Glivenko-Cantelli保持定理及权重校准技术之上。本文揭示这些工具的系统性本质，并将其整合为一个包含多个模块的系统，可通过模块化方式构建、共享与扩展。这种方法开发结构的变革使得相关方法可并行开发、复杂问题可协作求解，从而加速新型分析方法的研发。本文探讨四个相关推断问题：随机抽样参数估计、两阶段抽样、辅助信息融入及模型误设定。我们以半参数可加风险模型为对象，通过系统化构建针对上述四个相关推断问题的9个参数估计量与18个方差估计量，阐明这一模块化方法。模拟研究表明，这27个估计量获得的渐近结果均有效。最后，本文阐述该系统如何简化经验过程理论的应用——该理论虽强大但难以被广大方法开发者掌握。此外，本文讨论该系统的应用挑战及其向其他推断问题的拓展。