Selection of Auxiliary Variables for Three-Fold Linking Models in Small Area Estimation: A Simple and Effective Method

Song Cai,J.N.K Rao

doi:10.3390/stats5010009

Abstract

Model-based estimation of small area means can lead to reliable estimates when the area sample sizes are small. This is accomplished by borrowing strength across related areas using models linking area means to related covariates and random area effects. The effective selection of variables to be included in the linking model is important in small area estimation. The main purpose of this paper is to extend the earlier work on variable selection for area level and two-fold subarea level models to three-fold sub-subarea models linking sub-subarea means to related covariates and random effects at the area, sub-area, and sub-subarea levels. The proposed variable selection method transforms the sub-subarea means to reduce the linking model to a standard regression model and applies commonly used criteria for variable selection, such as AIC and BIC, to the reduced model. The resulting criteria depend on the unknown sub-subarea means, which are then estimated using the sample sub-subarea means. Then, the estimated selection criteria are used for variable selection. Simulation results on the performance of the proposed variable selection method relative to methods based on area level and two-fold subarea level models are also presented.

Highlights

Sample surveys are designed to provide reliable estimates of the overall means of a finite population and means for large domains or sub-populations
We report the performance of the proposed method with parameter-free transformation (3Fpfree ) and parameter-dependent transformation (3Fpdep )
A transformation-based method is proposed for selecting covariates under the threefold sub-subarea model for small area estimation

Summary

Introduction

Sample surveys are designed to provide reliable estimates of the overall means of a finite population and means for large domains or sub-populations (areas). For areas with small sample sizes (called small areas), direct area-specific estimators from the survey data are unreliable, and it is necessary to use model-based methods based on models linking area means to related covariates and random area effects. Resulting model-based estimators can lead to a significant increase in precision relative to direct estimators. Rao and Molina [1], in Chapter 6, provide a detailed account of model-based estimation under area level models. The effective selection of auxiliary variables to be included in the linking model is important for the success of model-based small area estimation (SAE). The area level model consists of two components: a sampling model given by yi = θi + ei , i = 1, . M and a linking model given by Licensee MDPI, Basel, Switzerland

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Conclusion