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arXiv · 1801.06739

Missing at random: a stochastic process perspective

Daniel Farewell·Rhian Daniel·Shaun Seaman
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Abstract

We offer a natural and extensible measure-theoretic treatment of missingness at random. Within the standard missing data framework, we give a novel characterisation 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 of the complete data: measurability conditions that suffice to ensure the likelihood factorisation necessary for ignorability. Our rigorous statement of the missing at random conditions also clarifies a common confusion: what is fixed, and what is random?

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Daniel Farewell, Rhian Daniel, Shaun Seaman. 2018-01-20. Missing at random: a stochastic process perspective. https://arxiv.org/abs/1801.06739

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