Testing Hypotheses for a Single Parameter
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Abstract
Basic concepts of hypothesis testing are presented in this Chapter. The Neyman-Pearson Lemma, which gives the form of the Most Powerful test for simple hypotheses, is introduced. This is then used as the building block for constructing the Uniformly Most Powerful tests and the Uniformly Most Powerful Unbiased tests. In this connection, special assumptions on the forms of the distribution of the data, such as the Monotone Likelihood Ratio, are presented. The focus is on testing of a scalar parameter.
References
- Allen, S. G. (1953). A class of minimax tests for one-sided composite hypothesies. The Annals of Mathematical Statistics. 24, 295–298.MathSciNetCrossRefGoogle Scholar
- Ferguson, T. S. (1967). Mathematical Statistics: A Decision Theoretic Approach. Academic.Google Scholar
- Karlin, S. and Rubin, H. (1956). The theory of decisin procedures for distributions with monotone likelihood ratio. Annals of Mathematical Statistics, 27, 272–299.MathSciNetCrossRefGoogle Scholar
- Lehmann, E. L. and Romano, J. P. (2005). Testing Statistical Hypotheses. Third edition. Springer.Google Scholar
- Neyman, J. and Pearson, E. S. (1933). On the problem of the most efficient tests of statistical hypotheses. Philosophy Transaction of the Royal Society of London. Series A. 231, 289–337.Google Scholar
- Neyman, J. and Pearson, E. S. (1936). Contributions to the theory of testing statistical hypothesis. Statistical Research Memois, 1, 1–37.Google Scholar
- Pfanzagl, J. (1967). A techincal lemma for monotone likelihood ratio families. The Annals of Mathematical Statistics, 38, 611–612.MathSciNetCrossRefGoogle Scholar
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