Detecting outliers and/or leverage points: a robust two-stage procedure with bootstrap cut-off points

Abstract

This paper presents a robust two-stage procedure for identification of outlying observations in regression analysis. The exploratory stage identifies leverage points and vertical outliers through a robust distance estimator based on Minimum Covariance Determinant (MCD). After deletion of these points, the confirmatory stage carries out an Ordinary Least Squares (OLS) analysis on the remaining subset of data and investigates the effect of adding back in the previously deleted observations. Cut-off points pertinent to different diagnostics are generated by bootstrapping and the cases are definitely labelled as good-leverage, bad-leverage, vertical outliers and typical cases. The procedure is applied to four examples.