{"paper":{"title":"Functional estimation and hypothesis testing in nonparametric boundary models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Markus Rei\\ss, Martin Wahl","submitted_at":"2017-08-09T14:28:47Z","abstract_excerpt":"Consider a Poisson point process with unknown support boundary curve $g$, which forms a prototype of an irregular statistical model. We address the problem of estimating non-linear functionals of the form $\\int \\Phi(g(x))\\,dx$. Following a nonparametric maximum-likelihood approach, we construct an estimator which is UMVU over H\\\"older balls and achieves the (local) minimax rate of convergence. These results hold under weak assumptions on $\\Phi$ which are satisfied for $\\Phi(u)=|u|^p$, $p\\ge 1$. As an application, we consider the problem of estimating the $L^p$-norm and derive the minimax separ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02854","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"}