{"paper":{"title":"Cram\\'er type moderate deviations for intermediate trimmed means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Nadezhda Gribkova","submitted_at":"2016-08-07T17:27:28Z","abstract_excerpt":"In this article we establish Cram\\'er type moderate deviation results for (intermediate) trimmed means $T_n=n^{-1} \\sum_{i=k_n+1}^{n-m_n}X_{i:n}$, where $X_{i:n}$ -- the order statistics corresponding to the first $n$ observations of a~sequence $X_1,X_2,\\dots $ of i.i.d random variables with $df$ $F$. We consider two cases of intermediate and heavy trimming. In the former case, when $\\max(\\alpha_n,\\beta_n)\\to 0$ ($\\alpha_n=k_n/n$, $\\beta_n=m_n/n$) and $\\min(k_n,m_n)\\to\\infty$ as $n\\to\\infty$, we obtain our results under a~natural moment condition and a~mild condition on the rate at which $\\alp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02246","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"}