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      • Department of Electrical and Electronics Engineering
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      Optimal decision rules for simple hypothesis testing under general criterion involving error probabilities

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      Author(s)
      Dulek, B.
      Öztürk, Cüneyd
      Gezici, Sinan
      Date
      2020
      Source Title
      IEEE Signal Processing Letters
      Print ISSN
      1070-9908
      Publisher
      IEEE
      Volume
      27
      Pages
      261 - 265
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      The problem of simple M-ary hypothesis testing under a generic performance criterion that depends on arbitrary functions of error probabilities is considered. Using results from convex analysis, it is proved that an optimal decision rule can be characterized as a randomization among at most two deterministic decision rules, each of the form reminiscent to Bayes rule, if the boundary points corresponding to each rule have zero probability under each hypothesis. Otherwise, a randomization among at most M(M-1)+1 deterministic decision rules is sufficient. The form of the deterministic decision rules are explicitly specified. Likelihood ratios are shown to be sufficient statistics. Classical performance measures including Bayesian, minimax, Neyman-Pearson, generalized Neyman-Pearson, restricted Bayesian, and prospect theory based approaches are all covered under the proposed formulation. A numerical example is presented for prospect theory based binary hypothesis testing.
      Keywords
      Hypothesis testing
      Optimal tests
      Convexity
      Likelihood ratio
      Randomization
      Permalink
      http://hdl.handle.net/11693/75431
      Published Version (Please cite this version)
      https://dx.doi.org/10.1109/LSP.2020.2966330
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      • Department of Electrical and Electronics Engineering 3702
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