{"paper":{"title":"Recovery of periodicities hidden in heavy-tailed noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","math.PR","math.ST","stat.TH"],"primary_cat":"math.CA","authors_text":"Illya M. Karabash, J\\\"urgen Prestin","submitted_at":"2015-12-29T17:18:38Z","abstract_excerpt":"We address a parametric joint detection-estimation problem for discrete signals of the form $x(t) = \\sum_{n=1}^{N} \\alpha_n e^{-i \\lambda_n t } + \\epsilon_t$, $t \\in \\mathbb{N}$, with an additive noise represented by independent centered complex random variables $\\epsilon_t$. The distributions of $\\epsilon_t$ are assumed to be unknown, but satisfying various sets of conditions. We prove that in the case of a heavy-tailed noise it is possible to construct asymptotically strongly consistent estimators for the unknown parameters of the signal, i.e., the frequencies $\\lambda_n$, their number $N$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08732","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}