{"paper":{"title":"Nonparametric estimation of multivariate convex-transformed densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Arseni Seregin, Jon A. Wellner","submitted_at":"2009-11-21T01:06:18Z","abstract_excerpt":"We study estimation of multivariate densities $p$ of the form $p(x)=h(g(x))$ for $x\\in \\mathbb {R}^d$ and for a fixed monotone function $h$ and an unknown convex function $g$. The canonical example is $h(y)=e^{-y}$ for $y\\in \\mathbb {R}$; in this case, the resulting class of densities [\\mathcal {P}(e^{-y})={p=\\exp(-g):g is convex}] is well known as the class of log-concave densities. Other functions $h$ allow for classes of densities with heavier tails than the log-concave class. We first investigate when the maximum likelihood estimator $\\hat{p}$ exists for the class $\\mathcal {P}(h)$ for var"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4151","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"}