Spring 2001 Seminar Series - April 24, 2001
University of Minnesota
School of Statistics
College of Liberal Arts

Dimension reduction for the conditional mean in regression

Bing Li
Department of Statistics
Penn State University

Tuesday, April 24, 2001
4:00 PM, 211 Vincent Hall
Minneapolis, East Bank Campus
Social at 3:30 PM, 300 Ford Hall

Abstract

In many situations regression analysis is mostly concerned with inferring about the conditional mean of the response given the predictor, and less concerned with the other aspects of the conditional distribution. In this paper we develop the dimension reduction methods that incorporate this consideration. We introduce the notion of the Central Mean Subspace (CMS), a natural inferential object for dimension reduction when the mean function alone is of interest. We will study the properties of the CMS, and develop various methods to estimate it. These methods include a new class of estimators which require fewer conditions than principal Hession dimensions (pHd), and which displays a clear advantage when one of the conditions for pHd is violated. CMS also reveals a transparent distinction among the existing methods for dimension reduction: Ordinary Least Square, principal Hessian dimension, Sliced Inverse Regression, and Sliced Averaged Variance Estimator. We will apply the new methods to a data set involving recumbent cows.