JSM 2005 Online Program

Abstract #304485

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:	364
Type:	Contributed
Date/Time:	Wednesday, August 10, 2005 : 8:30 AM to 10:20 AM
Sponsor:	General Methodology
Abstract - #304485
Title:	Equal Leverage via Robust Regression Using a Weighted Projection Matrix
Author(s):	Tamekia Jones*+ and David T. Redden
Companies:	University of Alabama at Birmingham and University of Alabama at Birmingham
Address:	University of Alabama at Birmingham, RPHB 327 , Birmingham, AL, 35294, United States
Keywords:	leverage ; projection matrix ; robust regression
Abstract:	Within linear regression, the diagonal of the projection matrix H = Xinv(X`X)X` defines leverage. Leverage can be conceptualized as both a measure of the deviation of an independent variable from the centroid of the independent variables and the relative contribution that an observation makes to its own predicted value. An observation with an extreme value on a predictor variable is called a point with high leverage. In small datasets, high leverage points can have an unusually large effect on the estimate of the regression coefficients, which can lead to poor approximations for the fitted regression line. We propose a robust regression method under the framework of weighted least squares. This method involves weighting all observations to obtain equal leverage among all observations. Equal leverage implies that all diagonal elements in the weighted projection matrix have equal value and each observation exerts the same amount of leverage on its predicted value. We present the derived properties of the regression model based on this weighted projection matrix and demonstrate these properties via simulations.

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