A new way for ranking functional data with applications in diagnostic test

This is a two faces paper. Firstly, it investigates diagnostic tests in situations when the observed variables are functional, that is, diagnostic tests that use functional variables as biomarkers. A procedure based on functional version of ROC analysis is proposed, the main question being linked with a suitable way for ranking the sample of functional data. The second facet of this paper is to present a general new way for ordering functional data in a self-contained way allowing for a wide scope of applications overpassing the former diagnostic test problem. Finite sample analysis highlight how this ranking procedure behaves for diagnostic test.