Likelihood inference in small area estimation by combining time-series and cross-sectional data

Using both time-series and cross-sectional data, a linear model incorporating autocorrelated random effects and sampling errors was previously proposed in small area estimation. However, in practice there are many situations that we have time-related counts or proportions in small area estimation; for example a monthly dataset on the number of incidences in small areas. The frequentist analysis of these complex models is computationally difficult. On the other hand, the advent of the Markov chain Monte Carlo algorithm has made the Bayesian analysis of complex models computationally convenient. Recent introduction of the method of data cloning has made frequentist analysis of mixed models also equally computationally convenient. We use data cloning to conduct frequentist analysis of small area estimation for Normal and non-Normal data situations with incorporating cross-sectional and time-series data. Another important feature of the proposed approach is to predict small area parameters by providing prediction intervals. The performance of the proposed approach is evaluated through several simulation studies and also by a real dataset.