Abstract
Design of a robust hypothesis test requires the simple hypotheses to be extended to the composite hypotheses via a suitable choice of uncertainty classes. The reader is referred to Sect. 2.2.2 for the fundamentals of robust hypothesis testing. In this chapter, minimax robust hypothesis testing is considered, where the uncertainty classes are built based on a single distance. From a single distance it is understood that the considered neighborhood classes accept only a single distance or a model.
The original version of this chapter was revised. An erratum to this chapter can be found at DOI 10.1007/978-3-319-49286-5_9.
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07 July 2017
An erratum has been published.
Notes
- 1.
In general \(\mathrm {arg}\sup \) may not always be achieved since \(\mathscr {G}_0\) and \(\mathscr {G}_1\) are non-compact sets in the topologies induced by the KL-divergence distance. In this book, existence of \(\hat{g}_0\) and \(\hat{g}_1\) is due to the KKT solution of the minimax optimization problem, which is introduced in Sect. 3.3.3.
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Gül, G. (2017). Robust Hypothesis Testing with a Single Distance. In: Robust and Distributed Hypothesis Testing. Lecture Notes in Electrical Engineering, vol 414. Springer, Cham. https://doi.org/10.1007/978-3-319-49286-5_3
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