{"paper":{"title":"Bootstrap confidence bands for spectral estimation of L\\'evy densities under high-frequency observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Daisuke Kurisu, Kengo Kato","submitted_at":"2017-05-01T16:48:58Z","abstract_excerpt":"This paper develops bootstrap methods to construct uniform confidence bands for nonparametric spectral estimation of L\\'{e}vy densities under high-frequency observations. We assume that we observe $n$ discrete observations at frequency $1/\\Delta > 0$, and work with the high-frequency setup where $\\Delta = \\Delta_{n} \\to 0$ and $n\\Delta \\to \\infty$ as $n \\to \\infty$. We employ a spectral (or Fourier-based) estimator of the L\\'{e}vy density, and develop novel implementations of Gaussian multiplier (or wild) and empirical (or Efron's) bootstraps to construct confidence bands for the spectral esti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00586","kind":"arxiv","version":4},"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"}