Hypothesis Testing
Abstract
Starting with the basic Neyman-Pearson Lemma for testing a simple hypothesis against a simple alternative, uniformly most powerful tests for one-sided problems in Monotone Likelihood Ratio families are constructed. To deal with two-sided problems and to test for one parameter in the presence of nuisance parameters, the concept of Unbiased Tests is introduced and Uniformly Most Powerful Unbiased Tests are constructed, mostly in the context of exponential families. For more general situations, Locally Best Tests are constructed. A Generalized Neyman-Pearson Lemma is needed to deal with all these problems. Other topics discussed in this chapter are p-values, Sequential Probability Ratio Tests, and confidence intervals. ...
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