Outlier detection under multicollinearity

Multicollinearity is a problem with dependence of regressors. In this paper, we investigate the functionality in identifying outliers of several robust methods based on residual weighting (least median of squares (LMS), least trimmed squares (LTS) and least weighted squares (LWS)) in the situation where the majority of the data suffer from multicollinearity. This is closely knit with the possibility of using LMS, LTS and LWS as tools for multicollinearity detection. It is shown that these methods fail in outlier detection (although they are ‘built’ for this purpose) with the increasing rate of multicollinearity. Theoretical results are also supported by a simulation study. Finally, we propose an alternative method, ridge LWS, that can be profitably used instead of LWS in the presence of multicollinearity.