Summary In this article, we propose a new method for estimating the randomisation (design‐based) mean squared error (DMSE) of model‐dependent small area predictors. Analogously to classical survey sampling theory, the DMSE considers the finite population values as fixed numbers and accounts for the MSE of small area predictors over all possible sample selections. The proposed method models the true DMSE as computed for synthetic populations and samples drawn from them, as a function of known statistics and then applies the model to the original sample. Several simulation studies for the linear area‐level model and the unit‐level mixed logistic model illustrate the performance of the proposed method and compare it with the performance of other DMSE estimators proposed in the literature.

Like in many countries, Israel has a fairly accurate population register at the national level, consisting of about 9 million persons (not including Israelis living abroad). However, the register is much less accurate for small geographical (statistical) areas, with an average area enumeration error of about 13%. The main reason for the inaccuracy at the area level is that people moving in or out of an area are often late in reporting their change of address, and in some cases, not reporting at all. In order to correct the errors at the area level in our next census, we investigate the use of the following three-step procedure: A-Draw a sample from an enhanced register to obtain initial direct sample estimates for the number of persons residing in each area on "census day", B-Fit the Fay-Herriot model to the direct estimates in an attempt to improve their accuracy, C-Compute a final census estimate for each statistical area as a linear combination of the estimate obtained in Step B and the register figure. We also consider a procedure to deal with not missing at random (NMAR) nonresponse in Step A. The proposed procedures are illustrated using data from the 2008 Census in Israel.