Outlier detection using robust measures of scale

Abstract

The studentized absolute maximum deviation from the mean statistic is modified by replacing the sample standard deviation with a biweight estimator of σ ². Simple approximate formulas for the 90 and 95th percentage points are found through the use of the Monte-Carlo technique. A comparison is made between the proposed procedure, the one using the sample standard deviation and the kurtosis measure (b₂ ), as methods for detecting one or more outliers. For normal slippage alternatives the use of the proposed procedure seems better than using standard deviation and about the same as using b₂ . For more general alternatives b₂ seems to be far more conservative than the proposed method. In addition, the proposed procedure can be used in one stage to detect multiple outliers, with only slight loss of power, as compared to consecutive use.

Keywords:

• Biweight
• Normality
• Outlier Detection
• Robustness
• Scale Estimators

Additional information

Notes on contributors

Jorge Martinez

On leave from the National Univeristy of Colombia