{"paper":{"title":"Minimax Goodness-of-Fit Testing in Multivariate Nonparametric Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Theofanis Sapatinas, Yuri I. Ingster","submitted_at":"2009-10-06T07:54:46Z","abstract_excerpt":"We consider an unknown response function $f$ defined on $\\Delta=[0,1]^d$, $1\\le d\\le\\infty$, taken at $n$ random uniform design points and observed with Gaussian noise of known variance. Given a positive sequence $r_n\\to 0$ as $n\\to\\infty$ and a known function $f_0 \\in L_2(\\Delta)$, we propose, under general conditions, a unified framework for the goodness-of-fit testing problem for testing the null hypothesis $H_0: f=f_0$ against the alternative $H_1: f\\in\\CF, \\|f-f_0\\|\\ge r_n$, where $\\CF$ is an ellipsoid in the Hilbert space $ L_2(\\Delta)$ with respect to the tensor product Fourier basis an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.0936","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"}