Robust estimation in finite population sampling using the conditional bias of a unit
David Haziza, University of Montreal
Abstract: In the context of classical statistics, Munoz-Pichardo, Munoz-Garcia, Moreno-Rebollo and Pino-Mejias
(1995) proposed to use the conditional bias as a measure of the influence of an observation. In this context,
it can be shown that the conditional bias is approximately proportional to the influence function (Hampel, 1974).
In survey sampling, there exist two frameworks for inference: the design-based framework and the model-based
framework. In both frameworks, the conditional bias of a unit can be easily obtained and can be used to justify
existing robust estimators or propose new robust estimators by downweighting the most influential units.
Using the conditional bias, we propose a robust estimator which reduces to an estimator very similar to the
one proposed by Chambers (1986) in the model-based framework and to the estimator proposed by Kokic and Bell
(1994) in the design-based framework under stratified simple random sampling. Our approach can be extended
easily to arbitrary sampling designs to obtain robust versions of the Horvitz-Thompson or generalized regression
estimators. In this talk, we will focus on the design-based framework but the model-based framework will be
briefly discussed.