Hypothesis Tests for Hypervolumes Under K-Dimensional ROC Manifold

• Activity Number: 656
• Type: Contributed
• Date/Time: Thursday, August 4, 2016 : 8:30 AM to 10:20 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Rajarshi Dey*
• Companies: University of South Alabama
• Keywords: ROC manifold ; Hypervolume ; U-statistic ; Permutation-like approach

Abstract

Consider any classification procedure for K groups based on a certain marker X. Let; Xi ? Fi; i=1,2,.,K where Fi is continuous for i= 1,2,.,K. The most common index to measure the performance of the marker is HUM (Hyper-volume Under Manifold) of the ROC (Receiver Operating Characteristic) manifold obtained by this marker. A random marker obtains an HUM of 1/K!. So, a natural setup for testing the performance of the marker is H0: HUM = 1/K! vs. HA: HUM > 1/K! . However, for even moderately large K; this test is useless as 1/K! is very small. I will discuss two new tests for testing the performance of a marker on a K(>2) group classification problem.