Principles of Hypothesis Testing
This chapter is devoted to some serious aspects of the hypothesis testing problems, including both the simple and composite cases. These consist of the fundamental lemma of Neyman-Pearson, in its abstract version due to Grenander, and a few of its applications as well as a technique in reducing composite hypotheses by means of weights. The latter contains a detailed Bayes methodology with iterated priors and some uniformity conditions that admit extensions to stochastic processes. Some of these considerations are classical, but they are seen to allow sharper analysis, in contrast with a use of the general (decision) theory, and these are examined carefully in the first four sections which also contain vector analysis approaches. It may be noted that this work demands an employment of deeper mathematical tools in solving some fundamental questions such as the Behrens-Fisher problem, and this is detailed in the fifth section. The last one is devoted to complementing the the preceding results, as exercises often with hints.
KeywordsCritical Region Vector Measure Similar Test Nuisance Parameter Powerful Region
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