Poverty estimation in small areas under random regression coefficient Poisson models
Policy makers need statistics of poverty indicators at disaggregated levels. However, small sample sizes pose a challenge in obtaining accurate estimates. Small Area Estimation is a field of statistics that uses mixed models to deal with these inference problems. Under an area-level random regression coefficient Poisson model, this work derives small area predictors of counts and proportions and introduces bootstrap estimators of the mean squared errors. The maximum likelihood estimators of the model parameters and the mode predictors of the random effects are calculated by a Laplace approximation algorithm. Simulation experiments are implemented to investigate the behavior of the fitting algorithm, the predictors and the mean squared error estimators with and without bias correction. The new statistical methodology is applied to data from the Spanish living conditions survey. The target is to estimate the proportions of women and men under the poverty line by province.
Palabras clave: small area estimation random coefficient Poisson regression models bootstrap poverty estimation.