{"paper":{"title":"Multidimensional multiscale scanning in Exponential Families: Limit theory and statistical consequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.ME","stat.TH"],"primary_cat":"math.PR","authors_text":"Axel Munk, Claudia K\\\"onig, Frank Werner","submitted_at":"2018-02-22T11:52:56Z","abstract_excerpt":"We consider the problem of finding anomalies in a $d$-dimensional field of independent random variables $\\{Y_i\\}_{i \\in \\left\\{1,...,n\\right\\}^d}$, each distributed according to a one-dimensional natural exponential family $\\mathcal F = \\left\\{F_\\theta\\right\\}_{\\theta \\in\\Theta}$. Given some baseline parameter $\\theta_0 \\in\\Theta$, the field is scanned using local likelihood ratio tests to detect from a (large) given system of regions $\\mathcal{R}$ those regions $R \\subset \\left\\{1,...,n\\right\\}^d$ with $\\theta_i \\neq \\theta_0$ for some $i \\in R$. We provide a unified methodology which control"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07995","kind":"arxiv","version":4},"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"}