Abstract #301980

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JSM 2003 Abstract #301980
Activity Number: 27
Type: Contributed
Date/Time: Sunday, August 3, 2003 : 2:00 PM to 3:50 PM
Sponsor: General Methodology
Abstract - #301980
Title: Moment-Based Dimension Reduction for Multivariate Response Regression
Author(s): Efstathia Bura*+ and Xiangrong Yin
Companies: George Washington University and University of Georgia
Address: Dept. of Statistics, Washington, DC, 20052-0001,
Keywords: dimension-reduction subspaces ; central subspaces ; regression graphics ; permutation tests
Abstract:

Dimension reduction aims to reduce the complexity of a regression without requiring a prespecified model. Central subspaces are designed to capture all the information for the regression and to provide a population structure for dimension reduction. In the case of multivariate response regressions, simple nonparametric inverse regression-based methods for the estimation of central subspaces, such as sliced inverse regression (SIR) and sliced average variance estimation (SAVE), are not very effective due to the curse of dimensionality. Covariance-based estimation methods for the kth moment based dimension reduction subspaces bypass slicing and do not suffer from the latter. In this article, the covariance-based method developed by Cook and Yin (2001) for univariate regressions is extended to multivariate response regressions and a new such method is proposed. Examples illustrating the theory are presented.

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