Estimation of Small Area Characteristics Using Multivariate Rao-Yu Model

The growing demand for high-quality statistical data for small areas coming from both the public and private sector makes it necessary to develop appropriate estimation methods. The techniques based on small area models that combine time series and cross-sectional data allow for efficient "borrowing strength" from the entire population and they can also take into account changes over time. In this context, the EBLUP estimation based on multivariate Rao-Yu model, involving both autocorrelated random effects between areas and sampling errors, can be useful. The efficiency of this approach involves the degree of correlation between dependent variables considered in the model. In the paper we take up the subject of the estimation of incomes and expenditure in Poland by means of the multivariate Rao-Yu model based on the sample data coming from the Polish Household Budget Survey and administrative registers. In particular, the advantages and limitations of bivariate models have been discussed. The calculations were performed using the sae and sae2 packages for R-project environment. Direct estimates were performed using the WesVAR software, and the precision of the direct estimates was determined using a balanced repeated replication (BRR) method.