Hypothesis tests in ordinal predictive models with optimal accuracy.

The article focuses on developing a novel hypothesis testing method, termed the jackknife empirical likelihood-ratio ordinal discrimination (JELOD) test, for optimizing multi-class ordinal predictive models by maximizing classification accuracy measured via the hypervolume under the ROC manifold (HUM). Addressing computational challenges in inference for optimal linear combinations of multiple predictors, the authors establish Wilks’ theorem for the test statistic, provide power analysis under Pitman alternatives, and introduce a network-based algorithm that reduces computational complexity from exponential to quadratic order. Extensive simulations demonstrate that JELOD controls type I error rates effectively, achieves higher power, and is computationally more efficient compared to existing parametric, Fréchet bound, and smoothed HUM methods. Application to an Alzheimer’s disease dataset with three ordered severity classes identifies significant neuropsychological biomarkers consistent with medical literature, and JELOD yields the most accurate classifier among competing methods. The paper also discusses limitations regarding high-dimensional covariates, unequal misclassification costs, unordered classes, and distributed data settings, suggesting directions for future research.