{"paper":{"title":"Goodness-of-fit test for noisy directional data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Claire Lacour (LM-Orsay), Thanh Mai Pham Ngoc (LM-Orsay)","submitted_at":"2012-03-09T07:34:37Z","abstract_excerpt":"We consider spherical data $X_i$ noised by a random rotation $\\varepsilon_i\\in$ SO(3) so that only the sample $Z_i=\\varepsilon_iX_i$, $i=1,\\dots, N$ is observed. We define a nonparametric test procedure to distinguish $H_0:$ ''the density $f$ of $X_i$ is the uniform density $f_0$ on the sphere'' and $H_1:$ ''$\\|f-f_0\\|_2^2\\geq \\C\\psi_N$ and $f$ is in a Sobolev space with smoothness $s$''. For a noise density $f_\\varepsilon$ with smoothness index $\\nu$, we show that an adaptive procedure (i.e. $s$ is not assumed to be known) cannot have a faster rate of separation than $\\psi_N^{ad}(s)=(N/\\sqrt{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2008","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"}