The use of auxiliary information in the linear least-squares prediction approach to cluster sampling in a finite population

Linear least-squares prediction methods are applied to cluster (two-stage) sampling problems in a finite population where auxiliary information is available. Two regression models which describe the behavior of the second-stage units and which utilize the auxiliary information are considered. For one model the optimum estimator of the total of the second-stage units and its mean square error (m.s.e.) are derived. The selection of clusters which minimize the m.s.e. are determined for certain cases. For both models a conventional estimator of the total is analyzed in the prediction theory framework. Optimum sampling designs for the conventional estimator are obtained for certain parameter configurations. A computer implemented study to compare the performances of the estimators for a wide range of parameter values is done. A practical problem is analyzed.