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A unified approach to outliers in the general linear model. (English) Zbl 0656.62078

In the normal general linear model \((Y,X\beta,\sigma^ 2V)\), with arbitrary known variance-covariance structure V, three types of outlier may be distinguished. The test-statistics and adjusted parameter estimates associated with each type of outlier are presented. A unified approach to outliers in the general linear model is developed, by showing that testing for the different types of outlier in the linear model \((Y,X\beta,\sigma^ 2V)\), is equivalent to testing for outliers in the linear model (ê,0,\(\sigma^ 2N)\), where \(\hat e\) is the vector of estimated residuals from the original model, and \(\sigma^ 2N\) is its variance-covariance matrix. A duality relationship between two types of outlier is exhibited. Corresponding to three types of outlier, three types of influence can be distinguished in the general linear model, and the influence measures of R. D. Cook [Technometrics 19, 15-18 (1977; Zbl 0371.62096)] and D. F. Andrews and D. Pregibon [J. R. Stat. Soc., Ser. B 40, 85-93 (1978; Zbl 0401.62025)] are generalized.

MSC:

62J05 Linear regression; mixed models
62H15 Hypothesis testing in multivariate analysis
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