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Abstract:
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Many classical dimension reduction methods---especially those based on inverse conditional moments---require the predictors to have elliptical distributions, or at least to satisfy a linearity condition. Such conditions, however, are too strong for some applications. We introduce a method to modify the existing dimension reduction estimators so that they no longer rely on such stringent conditions. This modification applies to all estimators based on inverse moments, such as Sliced Inverse Regression, Sliced Average Variance Estimator, and Directional Regression. We apply the new estimator to several data sets for which the predictors are non-elliptically distributed and the improvement is evident.
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