A Hybrid GREG Estimator for Estimation in Cluster Sampling

Abstract Cluster sampling is a widely used sampling design for survey data selection. The collected data provide information on both the individual units and the clusters. The parameter of interest is an unknown population total at the unit level. Due to the cluster sampling design, the model-assisted generalized regression estimator can be established either at the unit or at the cluster level. The unit-level estimator, however, ignores the cluster sampling design. The cluster-level estimator relies solely on the per-cluster aggregated information, which leads to the loss of individual patterns and the risk of ecological fallacy. As a remedy, in this paper we propose a hybrid generalized regression estimator as a new approach that balances between unit- and cluster-level modeling. It is implemented at the unit level like the study variable. However, in addition to the information of the units, it also takes into account the information of the other cluster members.