{"paper":{"title":"Adaptive density estimation for general ARCH models","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":"2006-09-27T08:38:33Z","abstract_excerpt":"We consider a model $Y\\_t=\\sigma\\_t\\eta\\_t$ in which $(\\sigma\\_t)$ is not independent of the noise process $(\\eta\\_t)$, but $\\sigma\\_t$ is independent of $\\eta\\_t$ for each $t$. We assume that $(\\sigma\\_t)$ is stationary and we propose an adaptive estimator of the density of $\\ln(\\sigma^2\\_t)$ based on the observations $Y\\_t$. Under various dependence structures, the rates of this nonparametric estimator coincide with the minimax rates obtained in the i.i.d. case when $(\\sigma\\_t)$ and $(\\eta\\_t)$ are independent, in all cases where these minimax rates are known. The results apply to various l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609745","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"}