Modern analysis by Kuttler, Kenneth

By Kuttler, Kenneth

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With λ denoting the log-likelihood for this model and λ = (λg , λh ), the resulting test statistic is ∂lλ ∂λ ∂lλ ∂λ I (λ) evaluated at λ = 0. 40). 41) , p = 1 known. The terms required for the test statistic are obtained from Cox (1961, p. 0858 . n The test statistic is ⎛ Tf = Tfg Tf h ⎝ σgg σgh σgh σhh ⎞−1 ⎛ ⎠ ⎝ Tfg ⎞ ⎠. 43) Tf h For regression models, Davidson and MacKinnon (1981) recommend the use of the J test (and its alternatives) to test for the true hypothesis against several alternatives at once.

J. Appl. Econ. : Testing separate families of hypotheses using right censored data. Commun. Stat. Simul. Comput. : Non-nested tests for competing models estimated by generalized method of moments. : The gradient statistic. Comput. Sci. Stat. : Testing model specification in seemingly unrelated regression models. Commun. Stat. Theory Meth. : Likelihood ratio test for model selection and non-nested hypotheses. Econometrika. : Tests of statistical hypotheses concerning several parameters when the number of observations is large.

43) Tf h For regression models, Davidson and MacKinnon (1981) recommend the use of the J test (and its alternatives) to test for the true hypothesis against several alternatives at once. 44) j=1 and performs a likelihood ratio test of the requirement that all γ j ( j = m) are zero. 44) to test the validity of a model m in the presence of several alternatives by means of a Wald test Jm for Hm : γ j = 0, j = 1, . . , M, j = m. He then argued that “if one of the models under consideration is the correct 2 distribution and the statistics of the other model, then its Jm statistic has a χ M−1 models diverge; if, instead, the correct model is not among the M models, then all statistics will diverge.

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