Design-consistent Domain Level Estimation in Surveys with Massive Nonresponse

Refusal of households in survey participation is becoming more frequent, and total nonresponse varies in subpopulations. Reweighting is performed in particular when information about nonrespondents is scarce. In survey practice, final sampling weights are defined in several stages: as the inverse of inclusion probabilities; then they are adjusted to reduce the bias in estimation due to unit nonresponse and undercoverage; eventually they are smoothed or trimmed, because the inflation of estimators' MSE is particularly severe at the domain level. In this paper, we deal with the design consistent estimation of domain parameters in surveys with massive nonresponse when the final sample is composed by two distinct parts drawn, with different designs, from two frames. We solve this problem of adapting a dual frame methodology by means of a simple model based on the Inverse Hypergeometric distribution. We also consider the smoothing of sampling weights. We propose a new trimming method, based on the Generalized Pareto distribution, which helps to improve the efficiency of estimators at the domain level.