{"paper":{"title":"Propagation of initial errors on the parameters for linear and Gaussian state space models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.OT","authors_text":"Salima El Kolei","submitted_at":"2013-03-14T17:13:44Z","abstract_excerpt":"For linear and Gaussian state space models parametrized by $\\theta_0 \\in \\Theta \\subset \\mathbb{R}^r, r \\geq 1$ corresponding to the vector of parameters of the model, the Kalman filter gives exactly the solution for the optimal filtering under weak assumptions. This result supposes that $\\theta_0$ is perfectly known. In most real applications, this assumption is not realistic since $\\theta_0$ is unknown and has to be estimated. In this paper, we analysis the Kalman filter for a biased estimator of $\\theta_0$. We show the propagation of this bias on the estimation of the hidden state. We give "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3518","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"}