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Given the location of a relative maximum of the log-likelihood function, how to assess whether it is the global maximum? This paper investigates a statistical tool, which answers this question by posing it as a hypothesis testing problem. A general framework for constructing tests for global maximum is given. The characteristics of the tests are investigated for two cases: correctly specified model and model mismatch. A finite sample approximation to the power is given, which gives a tool fordoi:10.1109/tit.2007.899537 fatcat:22ibnyoi55h5xgng7pyttxk7ne