Robust generalized regression estimation - ARCHIVED

The Best Linear Unbiased (BLU) estimator (or predictor) of a population total is based on the following two assumptions: i) the estimation model underlying the BLU estimator is correctly specified and ii) the sampling design is ignorable with respect to the estimation model. In this context, an estimator is robust if it stays close to the BLU estimator when both assumptions hold and if it keeps good properties when one or both assumptions are not fully satisfied. Robustness with respect to deviations from assumption (i) is called model robustness while robustness with respect to deviations from assumption (ii) is called design robustness. The Generalized Regression (GREG) estimator is often viewed as being robust since its property of being Asymptotically Design Unbiased (ADU) is not dependent on assumptions (i) and (ii). However, if both assumptions hold, the GREG estimator may be far less efficient than the BLU estimator and, in that sense, it is not robust. The relative inefficiency of the GREG estimator as compared to the BLU estimator is caused by widely dispersed design weights. To obtain a design-robust estimator, we thus propose a compromise between the GREG and the BLU estimators. This compromise also provides some protection against deviations from assumption (i). However, it does not offer any protection against outliers, which can be viewed as a consequence of a model misspecification. To deal with outliers, we use the weighted generalized M-estimation technique to reduce the influence of units with large weighted population residuals. We propose two practical ways of implementing M-estimators for multipurpose surveys; either the weights of influential units are modified and a calibration approach is used to obtain a single set of robust estimation weights or the values of influential units are modified. Some properties of the proposed approach are evaluated in a simulation study using a skewed finite population created from real survey data.