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**1 - 1**of**1**### TESTS FOR GLOBAL MAXIMUM OF THE LIKELIHOOD FUNCTION

"... Given a relative maximum of the log-likelihood function, how to assess whether it is the global maximum? In this paper we propose a statistical tool to answer this question by posing it as a hypothesis testing problem. A general framework for constructing tests for global maximum is given. The chara ..."

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Given a relative maximum of the log-likelihood function, how to assess whether it is the global maximum? In this paper we propose a statistical tool to answer 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 for performance prediction and a measure for comparison between tests. The tests are illustrated for two applications: estimating the parameters of a Gaussian mixture model and direction finding using an array of sensors- practical problems that are known to suffer from local maxima. 1.