The Detection of Influential Subsets in Linear Regression by Using an Influence Matrix

SUMMARY This paper presents a new method to identify influential subsets in linear regression problems. The procedure uses the eigenstructure of an influence matrix which is defined as the matrix of uncentred covariances of the effect on the whole data set of deleting each observation, normalized to include the univariate Cook statistics on the diagonal. It is shown that the eigenstructure of the influence matrix is useful to identify influential subsets and a procedure for detecting influential sets is proposed. The method is illustrated with two examples.