A model-calibration approach to using complete auxiliary information from survey data

Suppose that the finite population consists of N identifiable units. Associ ated with the ith unit are the study variable, y(1), and a vector of auxili ary variables, x(i). The values x(1),x(2),...,x(N) are known for the entire population (i.e., complete) bur y(i) is known only if the ith unit is sele cted in the sample. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this art icle, a unified model-assisted framework has been attempted using a propose d model-calibration technique. The proposed model-calibration estimators ca n handle any linear or nonlinear working models and reduce to the conventio nal calibration estimators of Deville and Sarndal and/or the generalized re gression estimators in the linear model case. The pseudoempirical maximum l ikelihood estimator of Chen and Sitter, when used in this setting, gives an estimator that is asymptotically equivalent to the model-calibration estim ator but with positive weights. Some existing estimators using auxiliary in formation are reexamined under this framework. The estimation of the finite population distribution function, using complete auxiliary information, is also considered, and estimators based on a general model are presented. Re sults of a limited simulation study on the performance of the proposed esti mators are reported.