Variable Selection for Fay-Herriot Models: A Cooperative Game Theory Approach

E. Cabello Garcia, J. C. Gonçalves Dosantos, D. Morales González, J. Sánchez Soriano

This paper presents a novel approach to variable selection in Small Area Estimation, focusing on the Fay-Herriot model. Traditional methods, such as those based on Akaike Information Criteria (AIC) and Kullback Information Criteria (KIC), often rely on stepwise selection and focus on the complete model, without individually examining the influence of auxiliary variables. The Shapley value of cooperative game theory is proposed to measure the importance of predictors. The Shapley value evaluates all possible combinations of auxiliary variables, ensuring an efficient average influence of the predictors. We study its performance through a simulation experiment, showing consistent identification of the true generating variables even under challenging conditions. An application to the Spanish Living Conditions Survey 2022 illustrates the method's practical application of the method for the estimation of poverty proportions in the Spanish provinces.

Keywords: Small Area Estimation, Shapley value, Bootstrap, Fay-Herriot, Poverty proportion

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June 13, 2025  11:00 AM
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