Adaptively transformed mixed‐model prediction of general finite‐population parameters

Abstract

For estimating area‐specific parameters (quantities) in a finite population, a mixed‐model prediction approach is attractive. However, this approach strongly depends on the normality assumption of the response values, although we often encounter a non‐normal case in practice. In such a case, transforming observations to make them suitable for normality assumption is a useful tool, but the problem of selecting a suitable transformation still remains open. To overcome the difficulty, we here propose a new empirical best predicting method by using a parametric family of transformations to estimate a suitable transformation based on the data. We suggest a simple estimating method for transformation parameters based on the profile likelihood function, which achieves consistency under some conditions on transformation functions. For measuring the variability of point prediction, we construct an empirical Bayes confidence interval of the population parameter of interest. Through simulation studies, we investigate the numerical performance of the proposed methods. Finally, we apply the proposed method to synthetic income data in Spanish provinces in which the resulting estimates indicate that the commonly used log transformation would not be appropriate.

Flexible Domain Prediction using Mixed Effects Random Forests

“…For instance, Rojas-Perilla et al (2020) generalise the EBP with a data-driven transformation on the dependent variable, such that normality assumptions can be met in transformed settings. Further details on how to obtain the most-likely transformation parameter that improves the performance of unit-level models are available in Rojas-Perilla et al (2020) and Sugasawa and Kubokawa (2019) or from a more applied perspective in Tzavidis et al (2018). Apart from transformation strategies, another alternative is the use of models with less restrictive (parametric) assumptions to avoid model-failure.…”

Flexible domain prediction using mixed effects random forests

“…For instance, Rojas-Perilla et al (2020) generalize the EBP with a data-driven transformation on the dependent variable, such that normality assumptions can be met in transformed settings. Further details on how to obtain the most-likely transformation parameter that improves the performance of unit-level models are available in Rojas-Perilla et al (2020) and Sugasawa & Kubokawa (2019) or from a more applied perspective in Tzavidis et al (2018). Apart from transformation strategies, another alternative is the use of models with less restrictive (parametric) assumptions to avoid model-failure.…”

Analysing Opportunity Cost of Care Work using Mixed Effects Random Forests under Aggregated Census Data

“…Without theoretical and practical considerations regarding violated assumptions, estimates are potentially biased and mean squared error (MSE) estimates are unreliable. In SAE, several strategies evolved to prevent model-misspecification: A well-known example is the assurance of normality by transforming the dependent variable (Sugasawa & Kubokawa, 2017;Tzavidis et al, 2018;Rojas-Perilla et al, 2019;Sugasawa & Kubokawa, 2019). Furthermore, the use of models under more flexible distributional assumptions is a fruitful approach (Diallo & Rao, 2018;Graf et al, 2019).…”