{"paper":{"title":"Asymptotic Theory for the Maximum of an Increasing Sequence of Parametric Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Jonathan B. Hill","submitted_at":"2017-07-09T10:24:53Z","abstract_excerpt":"\\cite{HillMotegi2017} present a new general asymptotic theory for the maximum of a random array $\\{\\mathcal{X}_{n}(i)$ $:$ $1$ $\\leq $ $i$ $\\leq $ $\\mathcal{L}\\}_{n\\geq 1}$, where each $\\mathcal{X}_{n}(i)$ is assumed to converge in probability as $n$ $\\rightarrow $ $\\infty $. The array dimension $\\mathcal{L}$ is allowed to increase with the sample size $n$. Existing extreme value theory arguments focus on observed data $\\mathcal{X}_{n}(i)$, and require a well defined limit law for $\\max_{1\\leq i\\leq \\mathcal{L}}|\\mathcal{X}_{n}(i)|$ by restricting dependence across $i$. The high dimensional ce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02555","kind":"arxiv","version":3},"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"}