Data‐driven transformations in small area estimation

Small area models typically depend on the validity of model assumptions. For example, a commonly used version of the empirical best predictor relies on the Gaussian assumptions of the error terms of the linear mixed regression model: a feature rarely observed in applications with real data. The paper tackles the potential lack of validity of the model assumptions by using data‐driven scaled transformations as opposed to ad hoc chosen transformations. Different types of transformations are explored, the estimation of the transformation parameters is studied in detail under the linear mixed regression model and transformations are used in small area prediction of linear and non‐linear parameters. The use of scaled transformations is crucial as it enables fitting the linear mixed regression model with standard software and hence it simplifies the work of the data analyst. Mean‐squared error estimation that accounts for the uncertainty due to the estimation of the transformation parameters is explored by using the parametric and semiparametric (wild) bootstrap. The methods proposed are illustrated by using real survey and census data for estimating income deprivation parameters for municipalities in the Mexican state of Guerrero. Simulation studies and the results from the application show that using carefully selected, data‐driven transformations can improve small area estimation.