October 13: Bradley Efron, Stanford University

SCHOOL OF STATISTICS
and
THE COLLEGE OF LIBERAL ARTS
UNIVERSITY OF MINNESOTA

BUEHLER-MARTIN DISTINGUISHED LECTURER SERIES
October 12, 13, and 14, 1999

Established by Mr. and Mrs. Thomas Martin
in Memory of
Robert J. Buehler, Professor of Statistics (1963-1988)

Assessing the Accuracy of Scatterplot Smoothers

Bradley Efron
Department of Statistics
Stanford University

Wednesday, October 13, 1999
4:00-5:00 PM, Room B25 Classroom Office Building, St. Paul
Social at 3:30 PM in Room 354 Classroom Office Building

Abstract

Suppose we observe n points (x, y) in the plane and wish to draw a smooth curve through them, say f (x), representing our assessment of the dependence of the conditional expectation E{y| x} on x. The traditional way to do this is by polynomial regression, perhaps fitting a linear, quadratic, or cubic function to the data via least squares. Scatterplot smoothers include more flexible ways of estimating the relationship between x and y, that operate locally in x, not requiring a global specification of f (x). Running means, running linear regressions, and spline smoothers are popular examples. We will consider the question of how accurate the function f (x) is as an estimate of the true regression E{y| x}. In actual applications the smoother is ``adapted'' to the problem at hand: some crucial parameter of the smoothing procedure such as the window width for a running mean is first selected on the basis of the n data points. Of particular concern is the effect of adaptation on the bias, variance and mean squared error of f (x).