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The consequences of the omission of possibly contaminated observations in a linear regression model for the performance of the ordinary least squares (LS‐) estimator are discussed. We compare the ordinary L Sestimator with the corresponding ‘never pooled’LS‐estimator with respect to the matrix‐valued mean squared error. Necessary and sufficient conditions are derived for the superiority of an estimator to another one and tests are proposed to check these conditions. Finally the resulting preliminary‐test‐estimators are investigated.

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