Bayesian small area estimation for skewed business survey variables

In business surveys, estimates of means and totals for subnational regions, industries\r\nand business classes can be too imprecise because of the small sample sizes that are\r\navailable for subpopulations.We propose a small area technique for the estimation of totals for\r\nskewed target variables, which are typical of business data. We adopt a Bayesian approach\r\nto inference. We specify a prior distribution for the random effects based on the idea of local\r\nshrinkage, which is suitable when auxiliary variables with strong predictive power are available:\r\nanother feature that is often displayed by business survey data. This flexible modelling of random\r\neffects leads to predictions in agreement with those based on global shrinkage for most of\r\nthe areas, but enables us to obtain less shrunken and thereby less biased estimates for areas\r\ncharacterized by large model residuals.We discuss an application based on data from the Italian\r\nsurvey on small and medium enterprises. By means of a simulation exercise, we explore the\r\nfrequentist properties of the estimators proposed. They are good, and differently from methods\r\nbased on global shrinkage remain so also for areas characterized by large model residuals.