Reweighting to Achieve Elliptically Contoured Covariates in Regression

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Abstract
We investigate a method of constructing weights to induce elliptically contoured covariates in regression analyses. Much recent work in regression has identified various data analytic and model robustness advantages associated with such covariates. In particular, new estimation methods like SIR, SIRII, SAVE, and PHD have been built around the assumption of elliptically contoured covariates. Finite samples of regression covariates may deviate from this ideal in practice, and the method developed here, termed Voronoi weighting, can be used to induce elliptical symmetry in such samples. In a number of examples, we show that reweighting cases by the Voronoi method can substantially enhance various procedures. For covariates that deviate from elliptical symmetry, we show that Voronoi weighting, in conjunction with some trimming via the minimum volume ellipsoid method, can be effective.

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