Robust Hypothesis Testing with a Single Distance
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.
KeywordsRobust Test Hellinger Distance Nominal Distribution Single Distance Uncertainty Class
- [DJ94]A. G. Dabak and D. H. Johnson, “Geometrically based robust detection,” in Proceedings of the Conference on Information Sciences and Systems, Johns Hopkins University, Baltimore, MD, May 1994, pp. 73–77.Google Scholar
- [GZ13b]G. Gül and A. M. Zoubir, “Robust hypothesis testing for modeling errors,” in Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), Vancouver, Canada, May 2013, pp. 5514–5518.Google Scholar
- [GZ14b]G. Gül and A. M. Zoubir, “Robust hypothesis testing with squared Hellinger distance,” in Proc. 22nd European Signal Processing Conference (EUSIPCO), Lisbon, Portugal, September 2014, pp. 1083–1087.Google Scholar
- [Wol96]E. Wolfstetter, “Stochastic dominance: Theory and applications,” 1996.Google Scholar