SIR: Dimension Reduction in the Presence of Linearly or Nonlinearly Related Predictors

Sufficient dimension reduction (sdr) is an effective tool for reducing highdimensional predictor spaces in regression problems. sdr achieves dimension reduction without loss of any regression information and without the need to assume any particular parametric form of a model. This is particularly useful for high-dimensional applications such as data mining, marketing, and bioinformatics. However, most sdr methods require a linearity condition on the predictor distribution, and that restricts the applications of sdr. In this article, we propose a new sdr method, sir3, which does not require the linearity condition, and which we show to be effective when nonlinearly-related predictors are present. sir3 is an extension of a representative sdr method sliced inverse regression (sir), and it is shown that sir3 reduces to sir when the linearity condition holds. A simulation study and a real data application are presented to demonstrate the effectiveness of the proposed method.