Year: 2024
Type: article
Abstract: The isotropic Cauchy distribution is a member of the central α-stable family that plays a role in the set of heavy-tailed distributions 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.
Source: Entropy
DOI: 10.3390/e26121084
Authors: Jihad Fahs, Ibrahim Abou-Faycal, Ibrahim Issa
Institution: American University of Beirut
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
Award: G8810037075
OpenAlex ID: W4405334097