Estimation in small areas, application to unemployment rate in Spanish provinces

Some methods for small area estimation are developed, using predictive approach for finite populations sampling. A model is built, using Royall theorem for optimal estimators, with the aim of estimating unemployment rate (an economic indicator for the site of the labour market) for provinces using greater Autonomous Communities estimations, from Spanish Active Population Survey, and some information about different auxiliary variables obtained by means of public registration or census. Validation of the model is discussed. Results obtained are better than those with usual design based sampling approach.