Small Area Estimation of Complex Parameters Under Unit-level Models with Skew-Normal Errors

Complex parameters, such as poverty indicators, are usually difficult to predict in small area estimation (SAE). Elbers et al. (2003) have proposed an empirical semi-parametric method for dealing with poverty indices in SAE. This method, commonly called the ELL method, consists of drawing from the empirical residuals to reconstitute the entire census. After simulating the census, any complex parameter is easily obtained. ELL method has poor MSE performance in many situations even though bias is usually small. Later, Molina and Rao (2010), proposed an empirical best predictor assuming the nested error linear regression model with normally distributed errors. As expected, this estimator can perform poorly when the model errors are not normally distributed. We relax the normality assumption by allowing the errors to follow a skew-normal distribution. Skew-normal (SN) is particularly interesting because it contains the normal distribution as a special case and at the same time it allows departure from symmetry. In this paper, empirical best (EB) estimators are derived assuming skew-normal errors and their performance in terms of MSE is studied relative to the normality-based and ELL predictors.