Linearisation for Variance Estimation by Means of Sampling Indicators: Application to Non‐response

In the presence of non‐response, it is usual to impute missing values, to reweight responding units and to adapt the estimators accordingly. The computation of the precision of the estimators becomes rapidly complex; it must take into account the sampling design, the treatment and the refinement of the estimators. In the absence of non‐response, it is possible to linearise estimators with respect to the sampling indicators to compute explicit variance estimators. In this paper, we extend this linearisation method to deal with non‐response. It becomes particularly straightforward to compute explicit variance estimators. Some known results are revisited in a simpler way than the usual developments, and new results for complex estimators are proposed. A simulation study evaluates the proposed methodology.