{"paper":{"title":"The Pareto Record Frontier","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.PR","authors_text":"Daniel Q. Naiman, James Allen Fill","submitted_at":"2019-01-17T05:03:26Z","abstract_excerpt":"For iid $d$-dimensional observations $X^{(1)}, X^{(2)}, \\ldots$ with independent Exponential$(1)$ coordinates, consider the boundary (relative to the closed positive orthant), or \"frontier\", $F_n$ of the closed Pareto record-setting (RS) region \\[ \\mbox{RS}_n := \\{0 \\leq x \\in {\\mathbb R}^d: x \\not\\prec X^{(i)}\\ \\mbox{for all $1 \\leq i \\leq n$}\\} \\] at time $n$, where $0 \\leq x$ means that $0 \\leq x_j$ for $1 \\leq j \\leq d$ and $x \\prec y$ means that $x_j < y_j$ for $1 \\leq j \\leq d$. With $x_+ := \\sum_{j = 1}^d x_j$, let \\[ F_n^- := \\min\\{x_+: x \\in F_n\\} \\quad \\mbox{and} \\quad F_n^+ := \\max\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.05620","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"}