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This paper reviews the most common situations where one or more regularityconditions which underlie classical likelihood-based parametric inference fail.We identify three main classes of problems: boundary problems, indeterminateparameter problems -- which include non-identifiable parameters and singularinformation matrices -- and change-point problems. The review focuses on thelarge-sample properties of the likelihood ratio statistic. We emphasizeanalytical solutions and acknowledge software implementations where available.We furthermore give summary insight about the possible tools to derivate thekey results. Other approaches to hypothesis testing and connections toestimation are listed in the annotated bibliography of the SupplementaryMaterial.

Likelihood Asymptotics in Nonregular Settings: A Review with Emphasis on the Likelihood Ratio