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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
Stable URL: http://www.jstor.org/stable/2669999
Page Count: 8
You can always find the topics here!Topics: Equation roots, Economic statistics, Sufficient conditions, Local maximum, Econometrics, Statistical theories, Mathematical maxima, Sample size, International economics, Roots of functions
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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.
Journal of the American Statistical Association © 1999 American Statistical Association