Optimal Auxiliary Variable Assisted Two-Phase Sampling Designs.

Two-phase sampling is a procedure in which sampling and data collection is conducted in two phases, aiming at achieving increased precision in estimation at reduced cost. The rst phase typically involves sampling a large number of elements and collecting data on variables that are easy to measure. In the second phase, a subset is sampled for which all variables of interest are observed. Utilization of the information provided by the data observed in the rst phase may increase precision in estimation by optimal selection of sampling design the second phase. This thesis deals with two-phase sampling when a random sample following some general parametric statistical model is drawn in the rst phase, followed by subsampling with unequal probabilities in the second phase. The method of maximum pseudo-likelihood estimation, yielding consistent estimators under general two-phase sampling procedures, is presented. The design in uence on the variance of the maximum pseudo-likelihood estimator is studied. Optimal subsampling designs under various optimality criteria are derived analytically and numerically using auxiliary variables observed in the rst sampling phase