The paper studies the applicability of area-level Poisson mixed models to
estimate small area counting indicators. Among the available procedures for fitting
generalized linear models, the method of moments (MM) and the penalised quasi-
likelihood (PQL) method are employed. The empirical best predictor (EBP) of the
area mean is derived using MM and compared with plug-in alternatives using MM
and PQL. The plug-in estimator using PQL is computationally faster and provides
competitive performance with respect to EBP that involves high complex integrals.
An approximation to the mean squared error (MSE) of the EBP is given and three
MSE estimators are proposed. The first two MSE estimators are plug-in estimators
without and with bias correction to the second order and the third one is based on
parametric bootstrap. Several simulation experiments are carried out for analysing
the behaviour of the EBP and for comparing the estimators of the MSE of the EBP.
A good choice in practice is the bootstrap alternative since it performs similarly to
the analytical versions and is computationally faster. The developed methodology and
software are applied to data from the 2008 Spanish living condition survey. The target
of the application is the estimation of poverty rates at province level.

• Empirical best prediction under area-level Poisson mixed models