{"paper":{"title":"Simultaneous confidence bands for Yule-Walker estimators and order selection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Moritz Jirak","submitted_at":"2012-05-30T12:26:48Z","abstract_excerpt":"Let $\\{X_k,k\\in{\\mathbb{Z}}\\}$ be an autoregressive process of order $q$. Various estimators for the order $q$ and the parameters ${\\bolds \\Theta}_q=(\\theta_1,...,\\theta_q)^T$ are known; the order is usually determined with Akaike's criterion or related modifications, whereas Yule-Walker, Burger or maximum likelihood estimators are used for the parameters ${\\bolds\\Theta}_q$. In this paper, we establish simultaneous confidence bands for the Yule--Walker estimators $\\hat{\\theta}_i$; more precisely, it is shown that the limiting distribution of ${\\max_{1\\leq i\\leq d_n}}|\\hat{\\theta}_i-\\theta_i|$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6644","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"}