The empirical likelihood is a powerful nonparametric tool, that emulates its parametric counterpart -- the parametric likelihood -- preserving many of its large-sample properties. This article tackles the problem of assessing the discriminatory power of three-class diagnostic tests from an empirical likelihood perspective. In particular, we concentrate on interval estimation in a three-class ROC analysis, where a variety of inferential tasks could be of interest. We present novel theoretical results and tailored techniques studied to efficiently solve some of such tasks. Extensive simulation experiments are provided in a supporting role, with our novel proposals compared to existing competitors, when possible. It emerges that our new proposals are extremely flexible, being able to compete with contestants and being the most suited to accommodating flexible distributions for target populations. We illustrate the application of the novel proposals with a real data example. The article ends with a discussion and a presentation of some directions for future research.

翻译：经验似然是一种强大的非参数工具，它模仿其参数对应物——参数似然——并保留其许多大样本性质。本文从经验似然的角度探讨评估三类诊断试验判别能力的问题。具体而言，我们聚焦于三类ROC分析中的区间估计，其中涉及多种可能感兴趣的推断任务。我们提出了新颖的理论结果和定制技术，以有效解决其中的部分任务。通过广泛的模拟实验提供支持，并在可能的情况下将我们的新方法与现有方法进行比较。结果表明，我们的新方法极为灵活，既能与现有方法竞争，又最适用于适应目标总体的灵活分布。我们通过一个真实数据示例展示了新方法的应用。文章最后讨论了未来研究的若干方向。