{"paper":{"title":"On the Pickands stochastic process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Adja Mbarka Fall, Gane Samb Lo","submitted_at":"2011-11-18T20:23:12Z","abstract_excerpt":"We consider the Pickands process {equation*} P_{n}(s)=\\log (1/s)^{-1}\\log \\frac{X_{n-k+1,n}-X_{n-[k/s]+1,n}}{% X_{n-[k/s]+1,n}-X_{n-[k/s^{2}]+1,n}}, {equation*} {equation*} (\\frac{k}{n}\\leq s^2 \\leq 1), {equation*} which is a generalization of the classical Pickands estimate $P_{n}(1/2)$ of the extremal index. We undertake here a purely stochastic process view for the asymptotic theory of that process by using the Cs\\\"{o}rg\\H{o}-Cs\\\"{o}rg\\H{o}-Horv\\'{a}th-Mason (1986) \\cite{cchm} weighted approximation of the empirical and quantile processes to suitable Brownian bridges. This leads to the unif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4469","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"}