{"paper":{"title":"Global uniform risk bounds for wavelet deconvolution estimators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Karim Lounici, Richard Nickl","submitted_at":"2011-03-08T10:40:09Z","abstract_excerpt":"We consider the statistical deconvolution problem where one observes $n$ replications from the model $Y=X+\\epsilon$, where $X$ is the unobserved random signal of interest and $\\epsilon$ is an independent random error with distribution $\\phi$. Under weak assumptions on the decay of the Fourier transform of $\\phi,$ we derive upper bounds for the finite-sample sup-norm risk of wavelet deconvolution density estimators $f_n$ for the density $f$ of $X$, where $f:\\mathbb{R}\\to \\mathbb{R}$ is assumed to be bounded. We then derive lower bounds for the minimax sup-norm risk over Besov balls in this esti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1489","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"}