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

In order to estimate the variance of estimators in survey sampling, we consider a method in which the estimators are linearized with respect to the basic random variables: the sampling indicator and the response indicator. When a superpopulation model is assumed, the estimators can also be linearized with respect to the variable of interest. This method ensures the derivation of a variance since the estimated parameters are linearized with respect to the random variables directly. It becomes particularly straightforward to construct explicit variance estimators. All sources of randomness are taken into account. The effects caused by the complexity of the estimation method, the calibration and the nonresponse treatment, imputation or reweighting, appear automatically and explicitly in the linearization variables. Through a set of examples, we show the simplicity of the method. Some results regarding the estimation of variance with nonresponse can be obtained in a simpler way than the usual developments. A set of simulations illustrates the proposed methodology.