Flexible empirical Bayes estimation of local fertility schedules: reducing small area problems and preserving regional variation

7 2.2 Properties of the empirical Bayes estimator The EB estimator can be expressed as the weighted sum of the means for each level of the hierarchical model.9 For the sake of simplicity, we review the EB estimator dened for a single age group. [...] Figure 3 shows the distribution of the bias from both two-level models relative to the bias of the three-level model.17 The relative bias is a ratio calculated as the RMSE of the two-level models divided by the RMSE of the three-level model. [...] For each simulation, the relative bias is calculated as the ratio of the RMSE of each two-level model relative to the RMSE of the three-level model. [...] As expected, we nd that the relative bias of the L2C-model increases with the level of regional variation (ϕ), while the opposite is the case for the L2R-model. [...] A relative bias of 1 means that the model prediction is the same as the bias of the three-level model and values higher than 1 mean that the predictions from the two-level model are more biased than those from the three-level model.