JSM 2005 Online Program

Abstract #304279

This is the preliminary program for the 2005 Joint Statistical Meetings in Minneapolis, Minnesota. Currently included in this program is the "technical" program, schedule of invited, topic contributed, regular contributed and poster sessions; Continuing Education courses (August 7-10, 2005); and Committee and Business Meetings. This on-line program will be updated frequently to reflect the most current revisions.

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Activity Number:	490
Type:	Contributed
Date/Time:	Thursday, August 11, 2005 : 8:30 AM to 10:20 AM
Sponsor:	General Methodology
Abstract - #304279
Title:	Fourier Methods for Estimating Dimension Reduction Subspace when the Distribution of Predictors Is Arbitrary
Author(s):	Yu Zhu*+ and Peng Zeng
Companies:	Purdue University and Purdue University
Address:	Statistics Department, West Lafayette, IN, 47907, United States
Keywords:	Regression ; Dimension reduction ; Fourier transform ; SIR ; SAVE
Abstract:	Dimension reduction is crucial for the success of general high-dimensional regression. Let Y and X denote the response and the predictor vector, respectively. A linear subspace S is a dimension reduction subspace for regressing Y on X if Y and X are independent conditional on PX, where P is the projection operator to S. The minimal dimension reduction subspace, when it exists, is defined to be the central subspace. In the literature, various methods, including SIR and SAVE, have been proposed to estimate the central subspace. All of these methods suffer from two limitations. First, it is not guaranteed that the whole central subspace can be recovered. Second, X has to satisfy some distributional constraints. In this talk, we propose a Fourier method for estimating the entire central subspace. Involving nonparametric estimation of the gradient of the log density of X, the method works for X, following arbitrary distribution. The asymptotic properties of the estimate of central subspace are discussed. Simulation study and a real example will be used to demonstrate the performance of this new method.

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