{"paper":{"title":"Approximation of Kolmogorov-Smirnov Test Statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Kalaj, Long Bai","submitted_at":"2018-02-24T18:13:48Z","abstract_excerpt":"Motivated by the weak limit of the Kolmogorov-Smirnov test statistics, in this contribution, we concern the asymptotics of \\begin{align*} \\mathbb{P}\\left\\{\\sup_{\\boldsymbol{x}\\in [0,1]^n}\\left(W(\\boldsymbol{x})\\Big| W(\\boldsymbol{1})=w\\right)>u\\right\\}, \\ w\\in\\mathbb{R}, \\end{align*} for large $u$ where $W(\\boldsymbol{x})$ is the multivariate Brownian sheet based on a distribution function $F$. The results related to general $F$ are investigated and some important examples are also showed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08883","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"}