Controling the bias of robust small area predictors

Joint work with Valéry Dongmo Jiongo (Statistics Canada) and Pierre Duchesne (University of Montreal)

 The user demand for small area estimators has been growing in most countries. This led survey statisticians to develop theoretically sound and yet practical estimation procedures, providing reliable estimators for small areas. A popular estimation method is the so-called empirical best linear unbiased prediction (EBLUP). However, the EBLUP is sensitive to the presence of outliers. That is, including or excluding outlying units from its computation may have a large impact on its magnitude. In recent years, the problem of robust small area estimation has received considerable interest. Sinha and Rao (2009) proposed estimation procedures designed for small areas, which are based on empirical best linear unbiased prediction estimators, properly modified in order to be robust to outliers. Also, bias-corrected estimators have been proposed by Chambers, Chandra, Salvati and Tzavidis (2009). In this talk, we introduce two new robust small area estimators that are robust to the presence of outliers. The first estimator is motivated by a decomposition similar in spirit to that of Chambers (1986) in the context of fixed effect models. Following Beaumont, Haziza and Ruiz-Gazen (2011), the second estimator is constructed using the estimated conditional bias of a unit, which can be interpreted as a measure of influence. The proposed robust estimators involve a psi-function, which depends on a tuning constant. The choice of this constant will be discussed. Finally, we will present the results of a simulation study that compares the performance of several robust estimators in terms of relative bias and relative efficiency.