A Model-Calibration Approach to Using Complete Auxiliary Information From Survey Data

Suppose that the Ž nite population consists of N identiŽ able units. Associated with the ith unit are the study variable, yi , and a vector of auxiliary variables, xi . The values x11 x21 : : : 1xN are known for the entire population (i.e., complete) but yi is known only if the ith unit is selected in the sample. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this article, a uniŽ ed model-assisted framework has been attempted using a proposed model-calibration technique. The proposed model-calibration estimators can handle any linear or nonlinear working models and reduce to the conventional calibration estimators of Deville and Särndal and/or the generalized regression estimators in the linear model case. The pseudoempirical maximum likelihood estimator of Chen and Sitter, when used in this setting, gives an estimator that is asymptotically equivalent to the model-calibration estimator but with positive weights. Some existing estimators using auxiliary information are reexamined under this framework. The estimation of the Ž nite population distribution function, using complete auxiliary information, is also considered, and estimators based on a general model are presented. Results of a limited simulation study on the performance of the proposed estimators are reported.