Influential observations in survey sampling

Abstract

If surveys are analysed using the randomisation distribution then model-based influence diagnostics have no role. Individual values can be influential in randomisation inference either when they are included in the sample or when they are not in the sample. In the former case diagnostics are useful, in the latter only prior knowledge can save the inference. Post-stratification unifies a variety of ad hoc procedures. Some ideas deducible from the influence function provide a justification for the Hajek ratio estimator which is an alternative to the Horvitz-Thompson estimator.