{"paper":{"title":"Risk bounds for the non-parametric estimation of L\\'{e}vy processes","license":"","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Christian Houdr\\'e, Jos\\'e E. Figueroa-L\\'opez","submitted_at":"2006-12-22T12:07:34Z","abstract_excerpt":"Estimation methods for the L\\'{e}vy density of a L\\'{e}vy process are developed under mild qualitative assumptions. A classical model selection approach made up of two steps is studied. The first step consists in the selection of a good estimator, from an approximating (finite-dimensional) linear model ${\\mathcal{S}}$ for the true L\\'{e}vy density. The second is a data-driven selection of a linear model ${\\mathcal{S}}$, among a given collection $\\{{\\mathcal{S}}_m\\}_{m\\in {\\mathcal{M}}}$, that approximately realizes the best trade-off between the error of estimation within ${\\mathcal{S}}$ and t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612697","kind":"arxiv","version":1},"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"}