Data-Driven Transformations in Small Area Estimation

Abstract

Summary 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.

Small Area Estimation of Poverty under Structural Change

“…Violations of the assumptions on the error term may be partly solved by allowing for more distributional flexibility in the response variable or the error term. Rojas-Perilla et al (2017) and the references therein provide various transformations of the response variable to achieve the validity of the assumption of identically and normally distributed error terms. A more comprehensive approach would be the application of…”

Domain Prediction with Grouped Income Data

“…Sugasawa and Kubokawa (2017)). Rojas-Perilla et al (2020) presented theoretical and numerical justifications for the use of data-driven transformations with unit-level SAE models. In particular, they propose an EBP approach with data-driven transformations where the data-driven transformation parameter is estimated by likelihood-based methods.…”

The R Package emdi for Estimating and Mapping Regionally Disaggregated Indicators

“…However, even after transformations, departures from normality may still exist in particular for the unit-level error term. For this reason, emdi also includes a variation of semi-parametric wild bootstrap (Flachaire 2005;Thai et al 2013;Rojas-Perilla et al 2019) to protect against departures from the model assumptions. The semi-parametric wild bootstrap is presented in detail in Appendix A.…”

“…A simulation study assessing the performance of the semi-parametric wild bootstrap is presented in Rojas-Perilla et al (2019).…”