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. Li and Dong (2009) introduced...

Regressions in which the fixed number of predictors p exceeds the number of independent observational units n occur in a variety of scientific fields. Sufficient dimension reduction provides a promising approach to such problems, by restricting attention to d  n linear combinations of the...