Abstract:
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We study likelihood ratio tests (LRTs) in submodels of multinomial models with simple null and general alternative hypotheses. If the dimension of the submodel is less than the dimension of the full model, then the restricted LRT is asymptotically more powerful against local alternatives than the unrestricted LRT. However, for every non-trivial dimensionality-restricted submodel, for any finite sample size, there exists simple null and alternative hypotheses, and a significance level for which the restricted LRT is less powerful than the unrestricted LRT.
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