Design-Based Treatment of Unit Nonresponse by the Calibration Approach

The use of nonresponse calibration weighting is considered in a complete design-based frameworkto account for the cases in which nonresponse is a fixed characteristic of the units, just like the interest variable. Approximate expressions of design-based bias and variance of the calibration estimator are derived and some estimators of the sampling variance are proposed. The choice of auxiliary variables is discussed from theoretical and practical point of view. The results of an extensive simulation study demonstrate how the reliability of the procedure is mainly determined by the capability of selecting auxiliary variables in such a way that their relationship with the interest variable is similar for both the respondent and nonrespondent sub-populations.