Unified predictor hypothesis tests in sufficient dimension reduction: A bootstrap approach

Abstract

In this paper, we newly define a unified predictor hypothesis that is applicable to all sufficient dimension reduction (SDR) methodologies. To test the predictor hypothesis, we propose a bootstrap approach by measuring the distances between reference subspaces and bootstrap subspaces. To measure the distances between two subspaces, the vector correlation coefficient is considered. Simulation studies confirm the background reasoning of the proposed tests. © 2010 The Korean Statistical Society.