{"paper":{"title":"Adaptive and minimax optimal estimation of the tail coefficient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Alexandra Carpentier, Arlene K.H. Kim","submitted_at":"2013-09-10T17:36:56Z","abstract_excerpt":"We consider the problem of estimating the tail index $\\alpha$ of a distribution satisfying a $(\\alpha, \\beta)$ second-order Pareto-type condition, where \\beta is the second-order coefficient. When $\\beta$ is available, it was previously proved that $\\alpha$ can be estimated with the oracle rate $n^{-\\beta/(2\\beta+1)}$. On the contrary, when $\\beta$ is not available, estimating $\\alpha$ with the oracle rate is challenging; so additional assumptions that imply the estimability of $\\beta$ are usually made. In this paper, we propose an adaptive estimator of $\\alpha$, and show that this estimator a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2585","kind":"arxiv","version":2},"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"}