A Procedure for Detecting a Pair of Outliers in Multivariate Dataset

Abstract

The paper presents a procedure for detecting a pair of outliers in multivariate data. The procedure involves a reduction of the dimensionality of the dataset to only two dimensions along outlier displaying components, and then determines the orientation of a least squares ellipse that fits the scatter of points of the two dimensional dataset. Finally, the reduced data is projected unto a vector which is determined in terms of the orientation of the ellipse. The results show that if two observations constitute a pair of outliers in a data set, then the pair is extreme at either ends of the one-dimensional projection and separated clearly from the remaining observations. If the two outliers are not distinct on such a one-dimensional projection, three key rules are prescribed for successful determination of the right pair of outliers.

Key words: Multiple Outlier Detection; Outlier Displaying Component