Sufficient Dimension Reduction Based on the Hellinger Integral: A General, Unifying Approach

• Activity Number: 593
• Type: Invited
• Date/Time: Thursday, August 4, 2011 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Xiangrong Yin*+ and Frank Critchley and Qin Wang
• Companies: University of Georgia and Open University and Virginia Commonwealth University
• Keywords: Sufficient dimension reduction ; Hellinger integral ; nonparametric estimation

Abstract

Sufficient dimension reduction provides a useful tool to study the dependence between a response and a multidimensional regressor, sliced regression (SR; Wang and Xia, 2008) being reported to have a range of advantages: estimation accuracy, exhaustiveness and robustness over many other methods. A new formulation is proposed here based on the Hellinger integral of order two, and so jointly local together with an efficient estimation algorithm. The link between Chi-squared-divergence and dimension reduction subspaces is the key to our approach, which has a number of strengths. It requires minimal (essentially, just existence) assumptions. Relatively faster to SR, allowing larger problems to be tackled, more general, multidimensional (discrete, continuous or mixed) response being allowed, and includes a sparse version enabling variable selection, while overall performance is broadly comparable, sometimes better. Finally, it unifies three existing methods, each being shown to be equivalent to adopting suitably weighted forms of the Hellinger integral.