High-Dimension, Low-Sample Size Mathematical Statistics

• Activity Number: 382
• Type: Invited
• Date/Time: Tuesday, August 3, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): J. S. Marron*+
• Companies: The University of North Carolina at Chapel Hill
• Keywords: HDLSS ; asymptotics ; mathematical statistics ; modern data

Abstract

High Dimension, Low Sample Size (HDLSS) data sets, and also some creative methods for their analysis, are rapidly proliferating. Mathematical statistical analysis in such contexts has been slower to follow, perhaps because the usual asymptotics are no longer relevant. It is seen that a more appropriate HDLSS asymptotic theory, based on fixed sample size, with increasing dimension, is perhaps surprisingly relevant and useful. Results so far fall into two classes. The first is the discovery that, modulo rotation, random HDLSS data have a rigid deterministic structure, which reveals a number of useful statistical insights. The second is a class of results studying commonly used estimators, such as principal component direction vectors, are either consistent or strongly inconsistent (i.e. the angle between to the direction being estimated tends to 90 degress), depending on the streg