October 14: 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)

Selection Criteria for Scatterplot Smoothers

Bradley Efron
Department of Statistics
Stanford University

Thursday, October 14, 1999
4:00-5:00 PM, Room L-110 Carlson School of Management
Social at 3:30 PM in Room 531 Heller Hall (formerly Management/Economics)

Abstract

Scatterplot smoothers estimate a regression function y = f (x) by local averaging of the observed data points (x(i), y(i)). In using a smoother the statistician must choose the ``window width'', a crucial parameter that says just how locally the averaging is done. The Cp criterion for selecting a window width is based on minimizing an unbiased estimate of prediction error. It is the most common selection method, but has been criticized for erratic behavior, sometimes selecting very small windows that give wiggly estimates of f (x).

We will discuss the Cp method in the context of an exponential family model that explains its erratic behavior. This will connect it with another selection criterion, Generalized Maximum Likelihood, a normal-theory empirical Bayes approach. Both methods, Cp and GML, are contained in a class of techniques each of which relates to a certain curved exponential family.