---

The boosting algorithm is a hybrid algorithm to reduce variance, a family of machine learning algorithms in supervised learning. This algorithm is a method to transform weak learning systems into strong systems based on the combination of different results. In this paper, mixture models with random effects are considered for small areas, where the errors follow the AR-GARCH model. To select the variable, machine learning algorithms, such as boosting algorithms, have been proposed. Using simulated and tax liability data, the boosting algorithm's performance is studied and compared with classical variable selection methods, such as the step-by-step method.