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Mismatched Binary Hypothesis Testing: Error Exponent Sensitivity

Accepted version
Peer-reviewed

Type

Article

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Authors

Abstract

We study the problem of mismatched binary hypothesis testing between i.i.d. distributions. We analyze the tradeoff between the pairwise error probability exponents when the actual distributions generating the observation are different from the distributions used in the likelihood ratio test, sequential probability ratio test, and Hoeffding's generalized likelihood ratio test in the composite setting. When the real distributions are within a small divergence ball of the test distributions, we find the deviation of the worst-case error exponent of each test with respect to the matched error exponent. In addition, we consider the case where an adversary tampers with the observation, again within a divergence ball of the observation type. We show that the tests are more sensitive to distribution mismatch than to adversarial observation tampering.

Description

Keywords

Testing, Probability distribution, Pairwise error probability, Error probability, Bayes methods, Training data, Signal processing algorithms, Hypothesis testing, mismatch, likelihood ratio test, generalized likelihood ratio test, sequenstial probability ratio test

Journal Title

IEEE Transactions on Information Theory

Conference Name

Journal ISSN

0018-9448
1557-9654

Volume Title

68

Publisher

Institute of Electrical and Electronics Engineers (IEEE)
Sponsorship
European Research Council (725411)