Unit‐Level Small Area Estimation With Inverse Hyperbolic Sine Transformation

Existing studies have investigated how transformations can be used to produce small area estimates for skewed variables. However, existing transformation‐based methods may be unsuitable for skewed variables containing non‐positive or extreme values. Motivated by these limitations, we propose a new method for constructing a unit‐level small area model using the inverse hyperbolic sine (IHS) transformation and develop an IHS‐based empirical Bayes (EB) predictor and its corresponding mean squared error (MSE) estimator. After determining an appropriate data scale through a scale sensitivity analysis, we use numerical simulations and an empirical study to demonstrate that the IHS‐based small area model generally outperforms competing models. Furthermore, the proposed method is robust across distributions and well suited to highly right‐skewed data.