{"paper":{"title":"High-dimensional nonparametric density estimation via symmetry and shape constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.CO","stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Min Xu, Richard J. Samworth","submitted_at":"2019-03-14T15:54:28Z","abstract_excerpt":"We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on $\\mathbb{R}^p$ and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and can mitigate the curse of dimensionality. Our main symmetry assumption is that the super-level sets of the density are $K$-homothetic (i.e. scalar multiples of a convex body $K \\subseteq \\mathbb{R}^p$). When $K$ is known, we prove that the $K$-homothetic log-concave maximum likelihood estimator based on $n$ independent observations from such a density has a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06092","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"}