A Model-Calibration Information-Theoretic Approach to Using Complete Auxiliary Information

Abstract:

      We propose a model-calibrated K-L relative entropy minimization (MKLEM) approach to using complete auxiliary information from survey data. Our estimator is asymptotically equivalent to a model-calibration (MC) estimator in Wu and Sitter (2001) in the case of estimating the finite population mean. One attractive advantage of our MKLEM approach is the intrinsic properties of the resulting weights: $\hat{p}_{i}>0$ and $\sum_{i\in s}\hat{p}_{i}=1$, which make this approach generally applicable to the estimation of distribution functions and quantiles. The resulting estimator $\hat{F}_{MKL}(y)$ is asymptotically equivalent to a generalized regression estimator and itself a distribution function.