Nonparametric Variable Transformation in Sufficient Dimension Reduction

Underlying many SDR techniques is a critical assumption that the predictors are elliptically contoured. When this assumption appears to be wrong, practitioners usually try variable transformation such that the transformed predictors become (nearly) normal.

The transformation function is often chosen from the log and power transformation family, as suggested in the celebrated Box–Cox model. However, any parametric transformation can be too restrictive, causing the danger of model misspecification. We suggest a nonparametric variable transformation method after which the predictors become normal.