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Resistant Dimension Reduction

Existing dimension reduction (DR) methods such as ordinary least squares (OLS) and sliced inverse regression (SIR) often perform poorly in the presence of outliers. Ellipsoidal trimming can be used to create outlier resistant DR methods that can also give useful results when the assumption of linearly related predictors is violated. Theory for SIR and OLS is reviewed, and it is shown that several important hypothesis tests for an important class of regression models can be done using OLS output originally meant for multiple linear regression.