Summary We offer a natural and extensible measure-theoretic treatment of missingness at random. Within the standard missing-data framework, we give a novel characterization of the observed data as a stopping-set sigma algebra. We demonstrate that the usual missingness-at-random conditions are equivalent to requiring particular stochastic processes to be adapted to a set-indexed filtration. These measurability conditions ensure the usual factorization of likelihood ratios. We illustrate how the theory can be extended easily to incorporate explanatory variables, to describe longitudinal data in continuous time, and to admit more general coarsening of observations.

中文翻译：

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随机缺失：随机过程视角

总结 我们提供了一种自然且可扩展的随机缺失测量理论处理方法。在标准缺失数据框架内，我们将观察到的数据描述为停止集 sigma 代数。我们证明了通常的随机缺失条件相当于要求特定的随机过程适应集合索引过滤。这些可测量性条件确保了似然比的通常分解。我们说明了如何轻松扩展该理论以包含解释变量，以连续时间描述纵向数据，并允许更一般地粗化观察。