{"paper":{"title":"Chebyshev polynomials, moment matching, and optimal estimation of the unseen","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Pengkun Yang, Yihong Wu","submitted_at":"2015-04-06T07:42:31Z","abstract_excerpt":"We consider the problem of estimating the support size of a discrete distribution whose minimum non-zero mass is at least $ \\frac{1}{k}$. Under the independent sampling model, we show that the sample complexity, i.e., the minimal sample size to achieve an additive error of $\\epsilon k$ with probability at least 0.1 is within universal constant factors of $ \\frac{k}{\\log k}\\log^2\\frac{1}{\\epsilon} $, which improves the state-of-the-art result of $ \\frac{k}{\\epsilon^2 \\log k} $ in \\cite{VV13}. Similar characterization of the minimax risk is also obtained. Our procedure is a linear estimator base"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01227","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"}