Unmasking Outliers and Leverage Points: A Confirmation

Abstract

Identification of multiple outliers and leverage points is difficult because of the masking effect. Recently, Rousseeuw and van Zomeren suggested using high-breakdown robust estimation methods—the least median of squares and minimum volume ellipsoid—for unmasking these observations. These methods tend to declare too many observations as extreme, however. A stepwise analysis is proposed here for confirmation of outliers and leverage points detected using the robust methods. Diagnostic measures are constructed for observations added back to the reduced sample. They are shown graphically. The complementary use of robust and diagnostic methods gives satisfactory results in analyzing two data sets. One data set consists often bad and four good leverage points. Four (or 10, using a different cutoff) extreme observations of the other data set (of size 28) are identified using the robust methods, but the stepwise analysis confirms only one. The limitations of Atkinson's confirmatory approach are discussed and illustrated.

Key Words:

• Adding-back plot
• Diagnostic measure
• High breakdown point
• Least median of squares
• Minimum volume ellipsoid
• Regression