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 model, a feature rarely observed in applications with real data. The present paper proposes to tackle 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 a linear mixed model and transformations are used in small area prediction of linear and non-linear parameters. The use of scaled transformations is crucial as it allows for fitting the linear mixed 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 using parametric and semi-parametric (wild) bootstrap. The proposed methods are illustrated using real survey and census data for estimating income deprivation parameters for municipalities in the Mexican state of Guerrero. Extensive simulation studies and the results from the application show that using carefully selected, data driven transformations can improve small area estimation.