Abstract
For two given general sources \( X = \left\{ {X^n } \right\}_{n = 1}^\infty \) and \( \bar X = \left\{ {\bar X^n } \right\}_{n = 1}^\infty \) we consider the hypothesis testing problem with the null hypothesis X and the alternative hypothesis X. This problem is also called the hypothesis testing X against X for simplicity. Here, both Xn and Xn are supposed to be Xn-valued random variables, where X denotes a source alphabet. In ordinary hypothesis testing problems we choose a subset A n C Xn as an acceptance region. If x, an output from one of the two sources, belongs to An, then we judge that the null hypothesis \( X = \left\{ {X^n } \right\}_{n = 1}^\infty \) is true. Otherwise, we judge that the alternative hypothesis \( \bar X = \left\{ {\bar X^n } \right\}_{n = 1}^\infty \) is true.
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© 2003 Springer-Verlag Berlin Heidelberg
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Han, T.S. (2003). Hypothesis Testing. In: Information-Spectrum Methods in Information Theory. Stochastic Modelling and Applied Probability, vol 50. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12066-8_4
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DOI: https://doi.org/10.1007/978-3-662-12066-8_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07812-5
Online ISBN: 978-3-662-12066-8
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