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Consider a 'needlet frame' $\\{\\phi_{j \\eta}\\}$ describing a localised projection onto the space of eigenfunctions of the Laplace operator on $\\mathbf M$ with corresponding eigenvalues less than $2^{2j}$, as constructed in \\cite{GP10}. We prove non-asymptotic concentration inequalities for the uniform deviations of the linear needlet density estimator $f_n(j)$ obtained from an empirical estimate of the needlet projection $\\sum_\\eta \\phi_{j "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1102.2450","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-11T22:01:17Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"db668175d94b41658a3eff2ccf52f8638eec2f5c18219807cb445fa9dd3d8ddb","abstract_canon_sha256":"97f6ca7823f3ed980589bdf95f7c882be7cc26fc7c56f74b364d818a12903a2a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:25.131244Z","signature_b64":"ebV14GWr+3yIOc9V6Atfgvtw9P1afD713fWY8yhg9pCPXWOA8W8RL8Asn4AxJxYH9nfxj/GKr7mFuPDDio0ODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c42d6949b1ad4f47bf3d6db3886389c7be63803a72e3569d91f7f86c85164134","last_reissued_at":"2026-05-18T03:48:25.130589Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:25.130589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Concentration Inequalities and Confidence Bands for Needlet Density Estimators on Compact Homogeneous Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Dominique Picard, Gerard Kerkyacharian, Richard Nickl","submitted_at":"2011-02-11T22:01:17Z","abstract_excerpt":"Let $X_1,...,X_n$ be a random sample from some unknown probability density $f$ defined on a compact homogeneous manifold $\\mathbf M$ of dimension $d \\ge 1$. 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