{"paper":{"title":"A double-indexed functional Hill process and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Gane Samb Lo, Modou Ngom","submitted_at":"2016-04-16T20:31:16Z","abstract_excerpt":"Let $X_{1,n} \\leq .... \\leq X_{n,n}$ be the order statistics associated with a sample $X_{1}, ...., X_{n}$ whose pertaining distribution function (% \\textit{df}) is $F$. We are concerned with the functional asymptotic behaviour of the sequence of stochastic processes \\begin{equation} T_{n}(f,s)=\\sum_{j=1}^{j=k}f(j)\\left(\\log X_{n-j+1,n}-\\log X_{n-j,n}\\right)^{s}, \\label{fme} \\end{equation} indexed by some classes $\\mathcal{F}$ of functions $f:\\mathbb{N}% ^{\\ast}\\longmapsto \\mathbb{R}_{+}$ and $s \\in ]0,+\\infty[$ and where $k=k(n)$ satisfies \\begin{equation*} 1\\leq k\\leq n,k/n\\rightarrow 0\\text"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04793","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"}