Authors:Nikos Tzavidis (University of Southampton)Cyril Favre-Martinoz (INSEE) (Speaker) David Haziza (University of Montreal)
Influential units occur frequently in surveys, especially in the context of business surveys that collect economic variables whose distribution are highly skewed. A unit is said to be influential when its inclusion or exclusion from the sample has an important impact on the magnitude of survey statistics. Robust small area prediction has received a lot of attention in recent years; see Gosh et al. (2008), Sinha and Rao (2009), Dongmo Jiongo et al. (2013), Chambers et al. (2013) and Fabrizi et al. (2014), among others. So far, researchers have mainly focused on unit level models and continuous characteristics of interest. Several robust versions of the empirical best linear unbiased predictor based on linear mixed models (LMM) have been proposed in the literature, including an M-quantile regression approach and an approach based on the concept of conditional bias of a unit. In practice, one must often face binary and count data. In this case, methods based on LMMs are not suited. We first propose a robust predictor in a general model-based framework with the use of generalized linear models and then we propose a unified framework for robust small area prediction in the context of generalized LMMs. We construct a general robust predictor based on the concept of conditional bias. We assess empirically the properties of the proposed robust estimator in terms of bias and efficiency.