  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.
