Nonparametric estimation and inference for polytomous discrimination index

Polytomous discrimination index is a novel and important diagnostic accuracy measure for multi-category classification. After reconstructing its probabilistic definition, we propose a nonparametric approach to the estimation of polytomous discrimination index based on an empirical sample of biomarker values. In this paper, we provide the finite-sample and asymptotic properties of the proposed estimators and such analytic results may facilitate the statistical inference. Simulation studies are performed to examine the performance of the nonparametric estimators. Two real data examples are analysed to illustrate our methodology.