Using Robust Scale Estimates in Detecting Multiple Outliers in Linear Regression

Abstract

SUMMARY Statistics for detecting outliers generally suffer from masking when multiple outliers are present. One aspect of this masking is inflation by the outliers of estimates of scale. This shrinks test statistics and results in loss of power to identify the outliers. Two familiar robust scale estimators are considered: the interquartile range (IR) and the median absolute deviation from the median (MAD). They are used here to scale statistics both for testing individual observations and for testing a no-outliers hypothesis. Some of these statistics use ordinary least squares residuals, others use recursive residuals calculated on adaptively ordered observations. The more severe the masking problem, the more advantageous robust scale estimation was found to be. IR and MAD worked equally well. Test statistics based on the recursive residuals were more powerful than those based on ordinary residuals.