On Prediction for Correlated Domains in Longitudinal Surveys

In the survey sampling estimation or prediction of both population’s and subopulation’s (domain’s) characteristics is one of the key issues. In the case of the estimation or prediction of domain’s characteristics one of the problems is looking for additional sources of information that can be used to increase the accuracy of estimators or predictors. One of these sources may be spatial and temporal autocorrelation. Due to the mean squared error (MSE) estimation, the standard assumption is that random variables are independent for population elements from different domains. If the assumption is taken into account, spatial correlation may be assumed only inside domains. In the paper, we assume some special case of the linear mixed model with two random components that obey assumptions of the first-order spatial autoregressive model SAR(1) (but inside groups of domains instead of domains) and first-order temporal autoregressive model AR(1). Based on the model, the empirical best linear unbiased predictor will be proposed together with an estimator of its MSE taking the spatial correlation between domains into account.