Abstract
Hypothesis tests for a vector-valued parameter are considered in this chapter. A single component of the parameter vector is of interest in the test, and the rest of the components the parameter vector are the “nuisance parameters.” The goal is to find a test that maximizes the power over all the components of the parameter vector. Because of the uniform nature of this optimality, it is possible only under rather restrictive conditions. Thus the Uniformly Most Powerful Unbiased tests are considered.
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References
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Lehmann, E. L. and Romano, J. P. (2005). Testing Statistical Hypotheses. Third edition. Springer.
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Li, B., Babu, G.J. (2019). Testing Hypotheses in the Presence of Nuisance Parameters. In: A Graduate Course on Statistical Inference. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-9761-9_4
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DOI: https://doi.org/10.1007/978-1-4939-9761-9_4
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