Testing the Isotropic Cauchy Hypothesis
Author Information
Author(s): Fahs Jihad, Abou-Faycal Ibrahim, Issa Ibrahim, Vitanov Nikolay Kolev
Primary Institution: American University of Beirut
Hypothesis
How does the performance of Likelihood Ratio Tests differ when testing isotropic Cauchy versus isotropic Gaussian distributions?
Conclusion
The study finds that the probability of error in detecting isotropic Cauchy distributions does not decay exponentially with the number of observations, contrary to the Gaussian case.
Supporting Evidence
- The isotropic Cauchy distribution is shown to have different error characteristics compared to the Gaussian distribution.
- Optimal Bayesian probabilities of error exhibit different asymptotic behaviors for the two distributions.
- The study provides a framework for understanding the performance of Likelihood Ratio Tests in the context of heavy-tailed distributions.
Takeaway
This study looks at how well we can tell the difference between two types of data distributions, one that is heavy-tailed and one that is more common. It shows that the usual methods don't work as well for the heavy-tailed type.
Methodology
The study uses Likelihood Ratio Tests to compare the performance of detecting isotropic Cauchy and Gaussian distributions based on a sequence of observations.
Limitations
The results may not generalize to all types of distributions beyond isotropic Cauchy and Gaussian.
Digital Object Identifier (DOI)
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