The Effective Use of Complete Auxiliary Information From Survey Data

A unified framework to deal with the effective use of complete auxiliary information from survey data at the estimation stage has been attempted. The proposed method involves modeling the relationship between the variable of interest and the auxiliary variables, and then incorporating the auxiliary information into design-consistent estimators of finite population means, totals, distribution functions and quantiles through the predicted values using calibration and empirical likelihood methods. The proposed model-calibration estimators can effectively handle any linear or non-linear models and the estimators of means and totals reduce to the generalized regression estimators under linear models. The pseudo-empirical likelihood approach (Chen and Sitter, 1999), when used in this setting, gives an estimator that is asymptotically equivalent to the model-calibration estimator but with positive weights, and therefore is preferred. Some existing estimators which use complete auxiliary information are shown to be special cases of this unified approach. The approach also provides a simple and elegant algorithm for obtaining an approximately generalized regression estimator with positive weights. This approach can be termed model-assisted as the resulting estimators are design-consistent regardless of the working model and particularly efficient if the working model adequately describes the true relationship in the population. Variance estimation and confidence intervals are also considered. Consistent analytical and jackknife variance estimators are obtained for estimators of means, totals and distribution functions. Small sample performance of these variance estimators has been investigated through a limited simulation study. Better conditional performance of the jackknife is highlighted. These variance estimates can be used in normal theory