{"paper":{"title":"Adaptive density deconvolution with dependent inputs","license":"","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Fabienne Comte (MAP5), J\\'er\\^ome Dedecker (LSTA), Marie-Luce Taupin (LM-Orsay)","submitted_at":"2006-06-07T19:00:30Z","abstract_excerpt":"In the convolution model $Z\\_i=X\\_i+ \\epsilon\\_i$, we give a model selection procedure to estimate the density of the unobserved variables $(X\\_i)\\_{1 \\leq i \\leq n}$, when the sequence $(X\\_i)\\_{i \\geq 1}$ is strictly stationary but not necessarily independent. This procedure depends on wether the density of $\\epsilon\\_i$ is super smooth or ordinary smooth. The rates of convergence of the penalized contrast estimators are the same as in the independent framework, and are minimax over most classes of regularity on ${\\mathbb R}$. Our results apply to mixing sequences, but also to many other dep"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606166","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"}