{"paper":{"title":"A functional Generalized Hill process and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"El Hadji Deme, Gane Samb Lo","submitted_at":"2011-11-16T22:39:40Z","abstract_excerpt":"We are concerned in this paper with the functional asymptotic behaviour of the sequence of stochastic processes\nT_{n}(f)=\\sum_{j=1}^{j=k}f(j)(\\log X_{n-j+1,n}-\\log X_{n-j,n}),\nindexed by some classes $\\mathcal{F}$ of functions $f:\\mathbb{N} \\backslash {0} \\longmapsto \\mathbb{R}_{+}$ and where $k=k(n)$ satisfies \n1\\leq k\\leq n,k/n\\rightarrow 0\\text{as}n\\rightarrow \\infty.\nThis is a functional generalized Hill process including as many new estimators of the extremal index when $F$ is in the extremal domain. We focus in this paper on its functional and uniform asymptotic law in the new setting of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3988","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"}