Resistance to Outliers of M-Quantile and Robust Random Effects Small Area Models

Abstract

The presence of outliers is a common feature in real data applications. It has been well established that outliers can severely affect the parameter estimates of statistical models, for example, random effects models, which can in turn affect the small area estimates produced using these models. Two outlier robust methodologies have been recently proposed in the small area literature. These are the M-quantile approach and the robust random effects approach. The M-quantile and robust random effects approaches are two distinct outlier robust small area methods and a comparison between these two methodologies is required. The present paper sets to fulfill this goal. Using model-based simulations and showing an application to real income data we examine how the alternative small area methodologies compare.

KEYWORDS:

• Influence function
• M-estimation
• Maximum likelihood estimation
• Multilevel model
• Weighted least squares

Mathematics Subject Classification:

• 62G35
• 62G39