Causal inference and finite population sampling

Abstract

In recent years, there has been a significant interest in causal inference in a potential outcomes framework, with applications to such diverse fields as sociology, behavioral sciences, biomedical sciences, and so on. The present work integrates causal inference with finite population sampling with a view to developing a unified theory. This is done with reference to a general assignment scheme of units to treatments, allowing randomization restrictions, and general linear unbiased estimators. Unbiased estimation of the sampling variance of treatment contrast estimators is explored under conditions milder that the age-old Neymannian strict additivity. The consequences of departure from such conditions are studied under the criteria of minimaxity and average bias. Finally, certain open issues are touched upon.