Robustness in Survey Sampling Using the Conditional Bias Approach with R Implementation

Abstract

The classical tools of robust statistics have to be adapted to the finite population context. Recently, a unified approach for robust estimation in surveys has been introduced. It is based on an influence measure called the conditional bias that allows to take into account the particular finite population framework and the sampling design. In the present paper, we focus on the design-based approach and we recall the main properties of the conditional bias and how it can be used to define a general class of robust estimators of a total. The link between this class and the well-known winsorized estimators is detailed. We also recall how the approach can be adapted for estimating domain totals in a robust and consistent way. The implementation in R of the proposed methodology is presented with some functions that estimate the conditional bias, calculate the proposed robust estimators and compute the weights associated to the winsorized estimator for particular designs. One function for computing consistently domain totals is also proposed.