Estimating small area mean with mixed and fixed effects support vector median regressions

Small area estimation has been extensively studied under linear mixed effects models. However, when the functional form of the relationship between the response and the covariates is not linear, it may lead to biased estimators of the small area parameters. In this paper, we relax the assumption of linear regression for the fixed part of the model and replace it by using the underlying concept of support vector quantile regression. This makes it possible to express the nonparametric small area estimation problem as mixed or fixed effects model regression. Through numerical studies we compare the efficiency of different models in estimating small area mean.