Semiparametric small area estimation for binary outcomes with application to unemployment estimation for Local Authorities in the UK

A new semiparametric and robust approach to small area estimation for discrete outcomes is proposed. The methodology represents an efficient and easily computed alternative to prediction using a generalised linear mixed model and is based on an extension of M- quantile regression. In addition, two estimators of the prediction mean squared error are described, one based on Taylor linearization and another based on block bootstrap. The proposed methodology is applied to UK annual Labour Force Survey data for estimating the proportion of the unemployed in Local Authorities in the UK. The properties of estimators are further empirically assessed in model-based simulations.