Robust inference in regression: a comparative study

Abstract

Outliers are observations of the response variable not consistent with any pattern or trend expressed by the remainder of the response data. It is well known that outliers in a multiple linear regression (MLR) analysis can distort the estimates of the unknown parameters. In addition, inferences made on parameters can also be adversely affected by outliers. In this paper, we study the impact of several types of outliers on the classical inferential techniques used in MLR. We also present several inferential procedures introduced in recent literature designed to be robust against outliers and propose two new alternative robust methods. The power of these robust procedures, along with the power of the classical methods, will then be compared in a simulation study.

Keywords:

• M-estimator
• bounded influence estimator
• robust inference
• iterated reweighted least squares
• robust generalized F test