Resumen de Model-based contributions to small area estimation
National statistical offices and private institutions are increasingly interested in having information on specific subgroups of the population. The main motivation is to address decision-making more effectively. Survey data are widely used for this purpose and no technical problem arises as long as the sample sizes are large enough to yield direct estimates of acceptable reliability. Otherwise, Small Area Estimation is an effective solution. This thesis contributes to this field using both area-level and unit-level models. First, new zero-inflated mixed models are proposed. Subsequently, the Fay-Herriot model is generalised and the unit-level multinomial logit mixed model is investigated. We predict segregation indexes and unemployment rates, respectively. Finally, the M-quantile regression is generalised to temporal data and the optimal selection of robustness parameters is addressed. In general, fitting algorithms are proposed and model-based predictors and mean squared error estimates are derived. Simulation studies and applications to real data are carried out to analyse the properties and applicability of the new statistical methods.
