{"paper":{"title":"A CLT for weighted time-dependent uniform empirical processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yuping Yang","submitted_at":"2014-12-28T13:24:13Z","abstract_excerpt":"For a uniform process $\\{ X_t: t\\in E\\}$ (by which $X_t $ is uniformly distributed on $(0,1)$ for $t\\in E$) and a function $w(x)>0$ on $(0,1)$, we give a sufficient condition for the weak convergence of the empirical process based on $\\{ w(x)(\\mathbb{1}_{X_t\\leq x} -x): t\\in E, x\\in [0,1]\\}$ in $\\ell^\\infty(E\\times [0,1])$. When specializing to $w(x)\\equiv 1$ and assuming strict monotonicity on the marginal distribution functions of the input process, we recover a result of Kuelbs, Kurtz, and Zinn (2013). In the last section, we give an example of the main theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8162","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"}