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Biometrika 1982 69(2):488-489; doi:10.1093/biomet/69.2.488
© 1982 by Biometrika Trust
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MISCELLANEA

A note on the use of residuals for detecting an outlier in linear regression

AJIT C. TAMHANE

Department of Industrial Engineering and Management Sciences, Northwestern University Evanston, Illinois, U. S.A

Consider the usual linear regression model y = Xß +{varepsilon}, where the vector {varepsilon} has E({varepsilon}) = 0, cov ({varepsilon}) = {sigma}2 V, where V is known. Let e = y-y be the least squares residual vector. It is shown that a test based on the transformed residual vector d* = V–1 e has, in the class of linear transformations of e, certain optimal power properties for detecting the presence of a single outlier when the label of the outlier observation is unknown. The outlier model considered here is that of shift in location.

Key Words: Linear regression • Outlier • Power • Residual


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