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, though other approaches to hypothesis testing and connections to estimation may be mentioned in passing. We emphasize analytical solutions and acknowledge software implementations where available. Some summary insight about the possible tools to derivate the key results is given.

翻译：本文综述了经典基于似然的参数推断所依赖的一个或多个正则条件失效的最常见情形。我们识别出三类主要问题：边界问题、不确定参数问题（包括不可识别参数和奇异信息矩阵）以及变点问题。综述重点聚焦于似然比统计量的大样本性质，尽管其他假设检验方法及与估计的联系也可能简要提及。我们强调解析解，并在可行时提及软件实现。文中还给出了关于推导关键结果的可能工具的一些总结性见解。