We describe a new design-based framework for drawing causal inference in randomized experiments. Causal effects in the framework are defined as linear functionals evaluated at potential outcome functions. Knowledge and assumptions about the potential outcome functions are encoded as function spaces. This makes the framework expressive, allowing experimenters to formulate and investigate a wide range of causal questions. We describe a class of estimators for estimands defined using the framework and investigate their properties. The construction of the estimators is based on the Riesz representation theorem. We provide necessary and sufficient conditions for unbiasedness and consistency. Finally, we provide conditions under which the estimators are asymptotically normal, and describe a conservative variance estimator to facilitate the construction of confidence intervals for the estimands.

翻译：我们描述在随机实验中进行因果关系推断的新的设计框架,将框架中的因果关系定义为根据潜在结果功能评估的线性功能,将关于潜在结果功能的知识和假设编码为功能空间,使框架具有表达性,使实验者能够拟订和调查一系列广泛的因果关系问题,我们描述的是使用框架界定的估计估计值的一类估计值,并调查其特性。估计值的构建以Riesz表示的方言为基础。我们为公正性和一致性提供了必要和充分的条件。最后,我们为估计值提供条件,使估计值处于无损正常状态,并描述保守的差异估计值,以便利为估计值构建信任间隔。