{"paper":{"title":"On a discrete Hill's statistical process based on sum-product statistics and its finite-dimensional asymptotic theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Gane Samb Lo","submitted_at":"2012-03-03T21:27:52Z","abstract_excerpt":"The following class of sum-product statistics\n  T_n(p)=\\frac{1}{k}\\sum_{h=1}^p \\sum_{(s_1...s_h)\\in P(p,h)} \\sum_{i_1=l+1}^{i_0} ... \\sum_{i_h=l+1}^{i_{h-1}}  i_h \\prod_{i=i_1}^{i_h} \\frac{(Y_{n-i+1,n}-Y_{n-i,n})^{s_i}}{s_i!}\n (where $l,$ $k=i_{0}$ and n are positive integers, $0<l<k<n,$ $P(p,h)$ is the set of all ordered parititions of $\\ p>0$ into $\\ h$ positive integers and $Y_{1,n}\\leq ...\\leq Y_{n,n}$ are the order statistics based on a sequence of independent random variables $Y_{1},$ $Y_{2},...$with underlying distribution $\\mathbb{P}(Y\\leq y)=G(Y)=F(e^{y})$), is introduced. For each p,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0685","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"}