|
Activity Number:
|
436
|
|
Type:
|
Contributed
|
|
Date/Time:
|
Wednesday, August 5, 2009 : 8:30 AM to 10:20 AM
|
|
Sponsor:
|
Section on Statistical Learning and Data Mining
|
| Abstract - #304796 |
|
Title:
|
Weighted Distance-Weighted Discrimination and Its Asymptotic Properties
|
|
Author(s):
|
Xingye Qiao*+ and Hao (Helen) Zhang and Yufeng Liu and Michael Jeremy Todd and J. Steve Marron
|
|
Companies:
|
The University of North Carolina at Chapel Hill and North Carolina State University and The University of North Carolina at Chapel Hill and Cornell University and The University of North Carolina at Chapel Hill
|
|
Address:
|
Hanes Hall B48, Chapel Hill, NC, 27599,
|
|
Keywords:
|
High dimension, low sample size data ; Linear discrimination ; Fisher consistency ; Nonstandard asymptotics ; Unbalanced data
|
|
Abstract:
|
While Distance-weighted Discrimination (DWD) is an appealing approach to classification in high dimensions, it was designed for balanced data sets. In the case of unequal costs, biased sampling or unbalanced data, there are major improvements available, using appropriately weighted versions of DWD. A major contribution of this paper is the development of optimal weighting schemes for various nonstandard classification problems. The second major contribution is substantial asymptotic study of the weighted DWD. Let $n$ be the sample size and $d$ be the dimension of data. Both high dimension low sample size asymptotics ($d$-asymptotics) and Fisher consistency of DWD are studied. The performance of the weighted DWD is evaluated on simulations and two real data examples. The theoretical results are also confirmed by simulations.
|
