Spring Seminar Series - April 30, 2003
University of Minnesota
School of Statistics
College of Liberal Arts
BUEHLER-MARTIN DISTINGUISHED LECTURER SERIES
Statistical Inference in High-Dimensional, Low Sample
Size Settings
Peter Hall
Australian National University
Wednesday, April 30,
2003
4:00 PM, 170
Tate Lab of Physics
Minneapolis, East
Bank Campus
Social at 3:30 PM,
300
Ford Hall
Abstract
Many contemporary discrimination problems in statistics involve the
analysis of samples which are considerably smaller than the lengths of the
vectors they contain. In such cases, conventional asymptotic arguments,
where model complexity remains fixed as sample size, n, increases, are obviously
unable to capture the character of discrimination methods. However, allowing
dimension to increase, for fixed n, reflects several of the essential features
of these problems, and provides insight into the relative performance of
different discrimination rules. Indeed, such an analysis produces simple,
low-dimensional geometric representations of the way in which discrimination
rules work for very high-dimensional data. Using these ideas we discuss
several discrimination methods, such as those based on the support vector
machine, distance-weighted discrimination and nearest neighbor techniques.