Variable importance assessments and backward variable selection for multi-sample problems

Abstract

Variable selection for multi-sample problems is of great interest in statistics. Existing methods for addressing this problem have some limits or disadvantages. In this paper, we propose distance-based variable importance measures to deal with these problems, which are inspired by the Multi-response permutation procedure (MRPP), Energy distance (ED) and Distance components (DISCO) analysis. The proposed variable importance assessments can effectively measure the importance of an individual dimension by quantifying its influence on the differences between multivariate distributions across treatment groups. An importance-measure-based backward selection (IM-BWS) algorithm is developed that can..