Détail du document
Identifiant
oai:arXiv.org:2408.06269
Sujet
Computer Science - Information The...Auteur
Fahs, Jihad Abou-Faycal, Ibrahim Issa, IbrahimCatégorie
Computer Science
Année
2024
Date de référencement
25/12/2024
Résumé
Isotropic $\alpha$-stable distributions are central in the theory of heavy-tailed distributions and play a role similar to that of the Gaussian density among finite second-moment laws.
Given a sequence of $n$ observations, we are interested in characterizing the performance of Likelihood Ratio Tests where two hypotheses are plausible for the observed quantities: either isotropic Cauchy or isotropic Gaussian.
Under various setups, we show that the probability of error of such detectors is not always exponentially decaying with $n$ with the leading term in the exponent shown to be logarithmic instead and we determine the constants in that leading term.
Perhaps surprisingly, the optimal Bayesian probabilities of error are found to exhibit different asymptotic behaviors.
Fahs, Jihad,Abou-Faycal, Ibrahim,Issa, Ibrahim, 2024, Testing the Isotropic Cauchy Hypothesis
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