JSM 2005 - Toronto

Abstract #304005

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 261
Type: Topic Contributed
Date/Time: Tuesday, August 9, 2005 : 10:30 AM to 12:20 PM
Sponsor: Biometrics Section
Abstract - #304005
Title: Transformation Methods for Dimension Reduction
Author(s): Shaoli Wang*+ and Bing Li
Companies: Yale University and The Pennsylvania State University
Address: 123 York ST Suite 2A, New Haven, CT, 06511, United States
Keywords: dimension reduction ; central subspace ; linearity condition ; iteration methods
Abstract:

Dimensionality is a major concern in many modern statistical problems. In regression analysis, dimension reduction aims to reduce the dimension of predictors without loss of information on the regression. In general, there are two key assumptions that may be required on the marginal distribution of predictor variables: a linearity condition and a constant variance condition. Among the existing dimension reduction methods, OLS, SIR, and IHT only require the first assumption, while PHD and SAVE require both assumptions. We propose General and Simple Iterative SAVE Transformation (GIST and SIST) methodology to estimate the central subspace. This methodology combines the information from SIR and SAVE methods, but requires only the linearity condition. We obtain the asymptotic distributions for GIST and SIST, thereby establishing a testing procedure for estimating the dimension of the central subspace. In this process, we also study the eigenvalue and eigenvector structure of iteration matrices, and thus reveal the mechanism that makes an iteration scheme work and the conditions under which iteration methods work best. In addition, we discuss higher-order iteration methods.

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Revised March 2005