A STEPWISE METHOD FOR THE IDENTIFICATION OF MULTIPLE OUTLIERS AND INFLUENTIAL OBSERVATIONS

A stepwise method is proposed to reduce the large computational burden for searching for multiple outliers and influential observations in regression. The method has an intuitive appeal for applied statisticians and can be employed easily. Its performance in analysing thirty-five data sets, of various sizes and dimensions, which commonly appear in the literature of regression diagnostics and robust regression, is promising. The method can successfully detect four high leverage points in a data set of which a high-breakdown robust estimator has difficulties. The saving in computational effort relative to the usual complete enumeration approach when searching for a group of up to four outliers and influential observations in a pollution data set of size 117 was of the order of one hundred-fold.