This paper reviews the most common situations where one or more regularity conditions which underlie classical likelihood-based parametric inference fail. We identify three main classes of problems: boundary problems, indeterminate parameter problems -- which include non-identifiable parameters and singular information matrices -- and change-point problems. The review focuses on the large-sample properties of the likelihood ratio statistic. We emphasize analytical solutions and acknowledge software implementations where available. We furthermore give summary insight about the possible tools to derivate the key results. Other approaches to hypothesis testing and connections to estimation are listed in the annotated bibliography of the Supplementary Material.

翻译：本文回顾了在经典基于似然的参数推断中，一个或多个正则性条件失效的最常见情形。我们识别出三大类问题：边界问题、不定参数问题（包括不可识别参数和奇异信息矩阵），以及变点问题。本综述重点关注似然比统计量的大样本性质。我们强调解析解，并列出可用的软件实现。此外，我们对推导关键结果的可能工具进行总结性阐述。关于假设检验的其他方法以及与估计的联系，在补充材料的注释式参考文献中列出。