Brazzale , Alessandra R. and Valentina , Mameli (2018) Likelihood Asymptotics in Nonregular Settings. A Review with Emphasis on the Likelihood Ratio. [Working Paper] WORKING PAPER SERIES, 4/2018 . , PADOVA
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We review the most common situations where one or some of the regularity conditions which underlie likelihood based parametric inference fail. Three main classes of problems will be treated: boundary problems, indeterminate parameters and singular information matrices, and change-point problems. The review is focused on the large- and small-sample properties of the likelihood ratio, though other approaches to hypothesis testing and connections to estimation will be mentioned in passing.
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