Robust estimation for finite populations based on a working model

A common scenario in finite population inference is that it is possible to find a working superpopulation model which explains the main features of th e population but which may not capture all the fine details. In addition, t here are often outliers in the population which do not follow the assumed s uperpopulation model. In situations like these, it is still advantageous to make use of the working model to estimate finite population quantities, pr ovided that we do it in a robust manner. The approach that we suggest is fi rst to fit the working model to the sample and then to fine-tune for depart ures from the model assumed by estimating the conditional distribution of t he residuals as a function of the auxiliary variable. This is a more direct approach to handling outliers and model misspecification than the Huber ap proach that is currently being used. Two simple methods. stratification and nearest neighbour smoothing, are used to estimate the conditional distribu tions of the residuals, which result in two modifications to the standard m odel-based estimator of the population distribution function, The estimator s suggested perform very well in simulation studies involving two types of model departure and have small variances due to their model-based construct ion as well as acceptable bias. The potential advantage of the proposed rob ustified model-based approach over direct nonparametric regression is also demonstrated.