{"paper":{"title":"Nonparametric inference on L\\'evy measures and copulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Axel B\\\"ucher, Mathias Vetter","submitted_at":"2012-05-02T13:15:33Z","abstract_excerpt":"In this paper nonparametric methods to assess the multivariate L\\'{e}vy measure are introduced. Starting from high-frequency observations of a L\\'{e}vy process $\\mathbf{X}$, we construct estimators for its tail integrals and the Pareto-L\\'{e}vy copula and prove weak convergence of these estimators in certain function spaces. Given n observations of increments over intervals of length $\\Delta_n$, the rate of convergence is $k_n^{-1/2}$ for $k_n=n\\Delta_n$ which is natural concerning inference on the L\\'{e}vy measure. Besides extensions to nonequidistant sampling schemes analytic properties of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0417","kind":"arxiv","version":2},"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"}