Small Area Estimation with a Lognormal Mixed Model under Informative Sampling

The demand for reliable business statistics at disaggregated levels, such as industry classes, increased considerably in recent years. Owing to small sample sizes for some of the domains, design-based methods may not provide estimates with adequate precision. Hence, modelbased small area estimation techniques that increase the effective sample size by borrowing strength are needed. Business data are frequently characterised by skewed distributions, with a few large enterprises that account for the majority of the total for the variable of interest, for example turnover. Moreover, the relationship between the variable of interest and the auxiliary variables is often non-linear on the original scale. In many cases, a lognormal mixed model provides a reasonable approximation of this relationship. In this article, we extend the empirical best prediction (EBP) approach to compensate for informative sampling, by incorporating design information among the covariates via an augmented modelling approach. This gives rise to the EBP under the augmented model. We propose to select the augmenting variable based on a joint assessment of a measure of predictive accuracy and a check of the normality assumptions. Finally, we compare our approach with alternatives in a model-based simulation study under different informative sampling mechanisms.

Empirical Best Prediction Under Unit-Level Logit Mixed Models

The article applies unit-level logit mixed models to estimating small-area weighted sums of probabilities. The model parameters are estimated by the method of simulated moments (MSM). The empirical best predictor (EBP) of weighted sums of probabilities is calculated and compared with plug-in estimators. An approximation to the mean-squared error (MSE) of the EBP is derived and a bias-corrected MSE estimator is given and compared with parametric bootstrap alternatives. Some simulation experiments are carried out to study the empirical behavior of the model parameter MSM estimators, the EBP and plug-in estimators and the MSE estimators. An application to the estimation of poverty proportions in the counties of the region of Valencia, Spain, is given.