A Test for Global Maximum

Abstract

In many applications of the maximum likelihood method people are bothered by the fact that there may be multiple roots to the likelihood equation, and therefore uncertain whether a root obtained corresponds to a global maximum of the likelihood function. In this talk, we give simple necessary and sufficient conditions for consistency and asymptotic optimality of a root to the likelihood equation. Based on the results, a large sample test is proposed for detecting whether a given root is consistent and asymptotically efficient, a property that is often possessed by the global maximizer of the likelihood function. A number of interesting examples, and the connection between the proposed test and the test of White (1982) for model misspecification will be discussed.

This work is joint with Prof. Li Gan of the University of Texas at Austin.

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