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Testing Hypotheses in the Presence of Nuisance Parameters

  • Bing LiEmail author
  • G. Jogesh Babu
Chapter
  • 2k Downloads
Part of the Springer Texts in Statistics book series (STS)

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.

References

  1. Ferguson, T. S. (1967). Mathematical Statistics: A Decision Theoretic Approach. Academic.Google Scholar
  2. Lehmann, E. L. and Romano, J. P. (2005). Testing Statistical Hypotheses. Third edition. Springer.Google Scholar
  3. Lehmann, E. L. and Casella, G. (1998). Theory of point estimation. Second edition. Springer, New York.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of StatisticsPenn State UniversityUniversity ParkUSA

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