Fall Seminar Series - November 6, 2003
University of Minnesota
School of Statistics
College of Liberal Arts
Contour regression: a general
approach to dimension reduction
Bing Li
Department of Statistics
The Pennsylvania State University
Thursday, November 6, 2003
4:00 PM, 115
Ford Hall
Minneapolis, East Bank
Campus
Social at 3:30 PM, 300
Ford Hall
Abstract
We propose a novel approach to sufficient dimension reduction in regression,
based on estimating contour directions of small variation in the response.
These directions span the orthogonal complement of the minimal space relevant
for the regression, and can be extracted according to two measures of variation
in the response, leading to Simple and General Contour Regression (SCR and
GCR) methodology. In comparison with existing sufficient dimension reduction
techniques, this contour-based methodology guarantees exhaustive estimation
of the central subspace under ellipticity of the predictor distribution
and mild additional assumptions, while maintaining square-root-of-n consistency
and computational ease. Moreover, it proves robust to departures from ellipticity.
We establish population properties for both SCR and GCR, and asymptotic
properties for SCR. Simulations to compare performance with that of standard
techniques such as ordinary least squares, sliced inverse regression, principal
Hessian directions, and sliced average variance estimation confirm the advantages
anticipated by the theoretical analyses. We demonstrate the use of contour-based
methods on a data set concerning Massachusetts colleges.
Joint work with Hongyuan Zha and Francesca Chiaromonte.