Abstract
This chapter deals with parametric test theory for a sample of independent and identically distributed observables. First, we introduce basic notions like null hypothesis, alternative hypothesis, errors of the first and of the second kind, significance level, and power. Then, we develop the theory of likelihood ratio tests, starting with the Neyman–Pearson lemma for testing simple hypotheses and some extensions to test problems with composite hypotheses. Based on exact distribution theory, Z-tests, t-tests, and chi-square tests are constructed for the parameters of a univariate normal distribution. Finally, likelihood ratio tests for general univariate exponential families are discussed and illustrated by means of several examples.
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Spokoiny, V., Dickhaus, T. (2015). Testing a Statistical Hypothesis. In: Basics of Modern Mathematical Statistics. Springer Texts in Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39909-1_6
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DOI: https://doi.org/10.1007/978-3-642-39909-1_6
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