USING ROBUST SCALE ESTIMATES IN DETECTING MULTIPLE OUTLIERS IN LINEAR-REGRESSION

Statistics for detecting outliers generally suffer from masking when m ultiple outliers are present. One aspect of this masking is inflation by the outliers of estimates of scale. This shrinks test statistics an d results in loss of power to identify the outliers. Two familiar robu st scale estimators are considered: the interquartile range (IR) and t he 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 ordinar y least squares residuals, others use recursive residuals calculated o n adaptively ordered observations. The more severe the masking problem , the more advantageous robust scale estimation was found to be. IR an d MAD worked equally well. Test statistics based on the recursive resi duals were more powerful than those based on ordinary residuals.