Diagnostics for comparing robust and least squares fits

Abstract

Is a simple least squares (LS) fit appropriate for the data at hand? How different would a more robust estimate be from LS? Is a high breakdown estimator necessary, or is a highly efficient robust estimator sufficient? We propose diagnostics which help answer these questions by measuring the difference in fits between least squares and, successively, a highly efficient robust estimate and a bounded influence robust estimate. Our diagnostic TDBETAS measures the overall change in parameter estimates among these three fits, while the casewise diagnostic CFITS measures change in individual fitted values. We also propose a plot based on CFITS which provides an effective graphical summary of underlying data structure.

Keywords:

• Bounded influence
• GR-estimates
• high breakdown
• linear model
• outlier
• regression diagnostics
• rank based methods
• R-estimates