{"paper":{"title":"Recursive Construction of Confidence Regions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Igor Cialenco, Tao Chen, Tomasz R. Bielecki","submitted_at":"2016-05-25T19:16:20Z","abstract_excerpt":"Assuming that one-step transition kernel of a discrete time, time-homogenous Markov chain model is parameterized by a parameter $\\theta\\in \\boldsymbol \\Theta$, we derive a recursive (in time) construction of confidence regions for the unknown parameter of interest, say $\\theta^*\\in \\boldsymbol \\Theta$. It is supposed that the observed data used in construction of the confidence regions is generated by a Markov chain whose transition kernel corresponds to $\\theta^*$ . The key step in our construction is derivation of a recursive scheme for an appropriate point estimator of $\\theta^*$. To achiev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08010","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"}