Sliced Inverse Mean Difference Regression for Sufficient Dimension Reduction

• Activity Number: 28
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Andreas Artemiou*+ and Lipu Tian
• Companies: Michigan Technological University and Michigan Technological University
• Keywords: Sliced Inverse Regression ; Cumulative Mean Estimation ; sufficient dimension reduction ; Order determination

Abstract

In this talk we create a new algorithm for sufficient dimension reduction. Our algorithm combines the ideas of slicing the response (see SIR by Li (1991)), the idea of cumulative estimation (see CUME by Zhu L.P., Zhu L. X. and Feng Z. H. (2010) JASA) and the idea of comparing points in different slices (see PSVM by Li, Artemiou and Li (2011)). At the same time our algorithm is different in the sense that it has the advantage of using all the points to find mean difference between slices instead of just portion of the points (like SIR and CUME did) at each iteration. We are also using inverse moments instead of SVM (like PSVM did). We also develop dimension determination tests. The good performance of our methodology is shown through simulations and data examples.