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

Ajit C. Tamhane

doi:10.1093/biomet/69.2.488

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

Ajit C. Tamhane^*

^*Corresponding author for this work

Industrial Engineering and Management Sciences

Research output: Contribution to journal › Comment/debate › peer-review

19 Scopus citations

Abstract

SUMMARY: Consider the usual linear regression model y = Xß +ε, where the vector ε has E(ε) = 0, cov (ε) = σ² V, where V is known. Let e = y-ŷ 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.

Original language	English (US)
Pages (from-to)	488-489
Number of pages	2
Journal	Biometrika
Volume	69
Issue number	2
DOIs	https://doi.org/10.1093/biomet/69.2.488
State	Published - Aug 1982

Keywords

Linear regression
Outlier
Power
Residual

ASJC Scopus subject areas

Statistics and Probability
Mathematics(all)
Agricultural and Biological Sciences (miscellaneous)
Agricultural and Biological Sciences(all)
Statistics, Probability and Uncertainty
Applied Mathematics

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T1 - A note on the use of residuals for detecting an outlier in linear regression

AU - Tamhane, Ajit C.

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N2 - SUMMARY: Consider the usual linear regression model y = Xß +ε, where the vector ε has E(ε) = 0, cov (ε) = σ2 V, where V is known. Let e = y-ŷ 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.

AB - SUMMARY: Consider the usual linear regression model y = Xß +ε, where the vector ε has E(ε) = 0, cov (ε) = σ2 V, where V is known. Let e = y-ŷ 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.

KW - Linear regression

KW - Outlier

KW - Power

KW - Residual

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DO - 10.1093/biomet/69.2.488

M3 - Comment/debate

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EP - 489

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 2

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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