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A Test for Global Maximum

Li Gan and Jiming Jiang
Journal of the American Statistical Association
Vol. 94, No. 447 (Sep., 1999), pp. 847-854
DOI: 10.2307/2669999
Stable URL: http://www.jstor.org/stable/2669999
Page Count: 8
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A Test for Global Maximum
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Abstract

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 often possessed by the global maximizer of the likelihood function. A number of examples, and the connection between the proposed test and the test of White for model misspecification, are discussed. Monte Carlo studies show that the test performs quite well when the sample size is large but may suffer the problem of overrejection with relatively small samples.

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