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

TLDR: In this article, a new method to identify influential subsets in linear regression problems is presented, which uses the eigenstructure of an influence matrix, 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.

Abstract: 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

Figures

Table 6. Cook's D Statistic for Multiple Cases and F Value for Outliers for the Hertzsprung-Russell Data.

Table 2. Largest Eigenvalue, Ratio to the Next one and Eigenvector for Example 1.

Table 4. Values of Cook's D for Multíple Cases and F Value for the International Phone Calls Data. The Notation {AlE} Means that Set B is Completly Deleted from the Analysis of the Influence of Set A.

Table 5. Eígenvector Coefficients Greater that .10 and Values of the D Statistic for the Hertzsprung-Russell Data of a Star Cluster.

Table 1. Data for Example 1.

Table 3. Elements oí First Eigenvector and Cook's Statistics for the International Phone Call Data.

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In this paper, a new method to identify infiuential subsets in linear regression problems is presented, which uses the eigenstructure of an infiuence matrix which is defined as the matrix defined by uncentered covariance.