{"paper":{"title":"Estimation in autoregressive model with measurement error","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Adeline Samson (MAP5), J\\'er\\^ome Dedecker (MAP5), Marie-Luce Taupin (SG)","submitted_at":"2011-05-06T15:45:17Z","abstract_excerpt":"Consider an autoregressive model with measurement error: we observe $Z_i=X_i+\\epsilon_i$, where $X_i$ is a stationary solution of the equation $X_i=f_{\\theta^0}(X_{i-1})+\\xi_i$. The regression function $f_{\\theta^0}$ is known up to a finite dimensional parameter $\\theta^0$. The distributions of $X_0$ and $\\xi_1$ are unknown whereas the distribution of $\\epsilon_1$ is completely known. We want to estimate the parameter $\\theta^0$ by using the observations $Z_0,..,Z_n$. We propose an estimation procedure based on a modified least square criterion involving a weight function $w$, to be suitably c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1310","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"}