Hypothesis tests in ordinal predictive models with optimal accuracy

In real-world applications involving multi-class ordinal discrimination, a common approach is to aggregate multiple predictive variables into a linear combination, aiming to develop a classifier with high prediction accuracy. Assessment of such multi-class classifiers often utilizes the hypervolume under ROC manifolds (HUM). When dealing with a substantial pool of potential predictors and achieving optimal HUM, it becomes imperative to conduct appropriate statistical inference. However, prevalent methodologies in existing literature are computationally expensive. We propose to use the jackknife empirical likelihood method to address this issue. The Wilks' theorem under moderate conditions is established and the power analysis under the Pitman alternative is provided. We also introduce a novel network-based rapid computation algorithm specifically designed for computing a general multi-sample $U$-statistic in our test procedure. To compare our approach against existing approaches, we conduct extensive simulations. Results demonstrate the superior performance of our method in terms of test size, power, and implementation time. Furthermore, we apply our method to analyze a real medical dataset and obtain some new findings.