Asymptotic Properties of Distance-Weighted Discrimination

While Distance-Weighted Discrimination (DWD) is an appeal ing 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 i mprovements available, using appropriately weighted versions of DWD. A major contributi on of this paper is the development of optimal weighting schemes for various nonstan dard classification problems. The second major contribution is substantial asymptotic st udy of both the original and the weighted DWD. Letn be the sample size and d be the dimension of data. Both conventional (n-asymptotic) Fisher consistency and high dimension low sam ple size asymptotics (d-asymptotics) are studied.