Small area models for skewed Brazilian business survey data
Summary 
The Brazilian Institute of Geography and Statistics performs an annual service survey that focuses on segments of the tertiary sector. Sample estimates for some economic activities in the north, north-east and midwest regions of Brazil have low precision due to the sample design. Furthermore, one of the main variables of interest is considerably skewed with potential outliers. To overcome this problem, skew normal and skew t-models are proposed to produce model-based estimates. The small domain estimation models relate operating revenue variables to potential auxiliary variables (the number of employed people and wages) obtained from a business register. The models proposed are compared with the usual Fay–Herriot model under the assumptions of known and unknown sampling variances and its transformed log-version under the assumption of known variances. The evaluation studies with real business survey data show that the models proposed seem to be more efficient for small area predictions under skewed data than the customarily employed Fay–Herriot model, as well as its log-normal version.