Small area estimation with subgroup analysis

In this article, a new unit level model based on a pairwise penalised regression approach is proposed for problems in small area estimation (SAE). Instead of assuming common regression coefficients for all small domains in the traditional model, the new estimator is based on a subgroup regression model which allows different regression coefficients in different groups. The alternating direction method of multipliers (ADMM) algorithm is used to find subgroups with different regression coefficients. We also consider pairwise spatial weights for spatial areal data. In the simulation study, we compare the performances of the new estimator with the traditional small area estimator. We also apply the new estimator to urban area estimation using data from the National Resources Inventory survey in Iowa.