{"paper":{"title":"On the Kozachenko-Leonenko entropy estimator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Nicolas Fournier, Sylvain Delattre","submitted_at":"2016-02-24T09:06:00Z","abstract_excerpt":"We study in details the bias and variance of the entropy estimator proposed by Kozachenko and Leonenko for a large class of densities on $\\mathbb{R}^d$. We then use the work of Bickel and Breiman to prove a central limit theorem in dimensions $1$ and $2$. In higher dimensions, we provide a development of the bias in terms of powers of $N^{-2/d}$. This allows us to use a Richardson extrapolation to build, in any dimension, an estimator satisfying a central limit theorem and for which we can give some some explicit (asymptotic) confidence intervals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07440","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"}