Large-Sample Theory for Likelihood Ratio Tests
The tests in Chapters 12 and 13 have strong optimality properties but require conditions on the densities for the data and the form of the hypotheses that are rather special and can fail for many natural models. By contrast, the generalized likelihood ratio test introduced in this chapter requires little structure, but it does not have exact optimality properties. Use of this test is justified by large-sample theory. In Section 17.2 we derive approximations for its level and power. Wald tests and score tests are popular alternatives to generalized likelihood ratio tests with similar asymptotic performance. They are discussed briefly in Section 17.4.
KeywordsLikelihood Ratio Test Tangent Space Maximum Likelihood Estimator Span Versus Likelihood Ratio Statistic
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