Estimation of small domain means for zero contaminated skewed data

For skewed data linear model assumptions are questionable. Consequently, the standard techniques for small domain estimation based on linear mixed model can be inefficient. The estimation methods for small domains for skewed data that are linear following a log-log transformation are investigated by Chandra and Chambers (2006). However, application of their methods is limited to strictly positive survey variables. In many surveys (e.g. business and enterprises, income and expenditure, agricultural and ecological surveys etc) variables that are skewed often take zero values. In this paper we introduce small domain estimation techniques for skewed data in presence of zeros. In this context, following Fletcher et at. (2005) and Karlberg (2000) we extend Chandra and Chambers (2006) approach of small domain estimation under a mixture model. Our empirical results show the method works well and produces an efficient set of small area estimates.