Reweighting to achieve elliptically contoured covariates in regression

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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.

Original languageEnglish (US)
Pages (from-to)592-599
Number of pages8
JournalJournal of the American Statistical Association
Issue number426
StatePublished - Jun 1994

Bibliographical note

Funding Information:
* R. Dennis Cook is Professor, Department of Applied Statistics, University of Minnesota, St. Paul, MN 55108. Christopher Nachtsheim is Professor and Chair, Curtis L. Carlson School of Management, University of Min- nesota, Minneapolis, MN 55455. This work was supported in part by National Science Foundation Grant DMS-92 124 13 awarded to R. Dennis Cook. The authors thank the referee for many helpful comments on an earlier version.

Copyright 2015 Elsevier B.V., All rights reserved.


  • Monte Carlo sampling
  • SAVE
  • Sliced inverse regression
  • Voronoi tesselation


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