{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:GZCDQCMTYOXPTQAJP5VVOETEYX","short_pith_number":"pith:GZCDQCMT","canonical_record":{"source":{"id":"1210.1715","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-10-05T11:36:43Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"224309ee136d50af512b3542870f067f3114904aad54c61d7d9415f9a42ce6a7","abstract_canon_sha256":"08ee6f5211f44510b9e68653d8b80ce2d3d15d01666dc4d1d8cd0b2185d198ff"},"schema_version":"1.0"},"canonical_sha256":"3644380993c3aef9c0097f6b571264c5fb99b59ede2d31ff84fa7303aecc847d","source":{"kind":"arxiv","id":"1210.1715","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.1715","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"arxiv_version","alias_value":"1210.1715v2","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1715","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"pith_short_12","alias_value":"GZCDQCMTYOXP","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GZCDQCMTYOXPTQAJ","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GZCDQCMT","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:GZCDQCMTYOXPTQAJP5VVOETEYX","target":"record","payload":{"canonical_record":{"source":{"id":"1210.1715","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-10-05T11:36:43Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"224309ee136d50af512b3542870f067f3114904aad54c61d7d9415f9a42ce6a7","abstract_canon_sha256":"08ee6f5211f44510b9e68653d8b80ce2d3d15d01666dc4d1d8cd0b2185d198ff"},"schema_version":"1.0"},"canonical_sha256":"3644380993c3aef9c0097f6b571264c5fb99b59ede2d31ff84fa7303aecc847d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:45.346738Z","signature_b64":"WckfdqqhQX5MuMfO+yUYUVjG9h0QbqPCSzkXoVIa2Rwb9PhH8k4pz6QS1Gu3j4mBOAhjLk9YRefM6i1cttnRDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3644380993c3aef9c0097f6b571264c5fb99b59ede2d31ff84fa7303aecc847d","last_reissued_at":"2026-05-18T03:20:45.346083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:45.346083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.1715","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:20:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ltvDvu4nuQTGxutdcAqDocp171+AQBZ4UBYCfW9Jmesgdc6gZ4MJ554qSD2bTHRielwYAovFYyRK18z3yzhhAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:51:28.240422Z"},"content_sha256":"d1716633a9858bd4181cb28c6444c40c1a3746259e17e42ab1a74767e7277c5d","schema_version":"1.0","event_id":"sha256:d1716633a9858bd4181cb28c6444c40c1a3746259e17e42ab1a74767e7277c5d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:GZCDQCMTYOXPTQAJP5VVOETEYX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On adaptive minimax density estimation on $R^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"A. Goldenshluger, O. Lepski","submitted_at":"2012-10-05T11:36:43Z","abstract_excerpt":"We address the problem of adaptive minimax density estimation on $\\bR^d$ with $\\bL_p$--loss on the anisotropic Nikol'skii classes. We fully characterize behavior of the minimax risk for different relationships between regularity parameters and norm indexes in definitions of the functional class and of the risk. In particular, we show that there are four different regimes with respect to the behavior of the minimax risk. We develop a single estimator which is (nearly) optimal in orderover the complete scale of the anisotropic Nikol'skii classes. Our estimation procedure is based on a data-drive"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1715","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:20:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mXxIPwcZx0ydj44UkPK5SBxGey/W9BnQW/0iJBUQWAFvc5UQSyjLX99u5r9KXp1/vL5hPoAuJDxkvtK+6Cp8Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:51:28.240764Z"},"content_sha256":"e5755b8934b37710b128ec1cee3a842148ae3ba0ef7be168ad618fdf647182e0","schema_version":"1.0","event_id":"sha256:e5755b8934b37710b128ec1cee3a842148ae3ba0ef7be168ad618fdf647182e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GZCDQCMTYOXPTQAJP5VVOETEYX/bundle.json","state_url":"https://pith.science/pith/GZCDQCMTYOXPTQAJP5VVOETEYX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GZCDQCMTYOXPTQAJP5VVOETEYX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T12:51:28Z","links":{"resolver":"https://pith.science/pith/GZCDQCMTYOXPTQAJP5VVOETEYX","bundle":"https://pith.science/pith/GZCDQCMTYOXPTQAJP5VVOETEYX/bundle.json","state":"https://pith.science/pith/GZCDQCMTYOXPTQAJP5VVOETEYX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GZCDQCMTYOXPTQAJP5VVOETEYX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GZCDQCMTYOXPTQAJP5VVOETEYX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"08ee6f5211f44510b9e68653d8b80ce2d3d15d01666dc4d1d8cd0b2185d198ff","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-10-05T11:36:43Z","title_canon_sha256":"224309ee136d50af512b3542870f067f3114904aad54c61d7d9415f9a42ce6a7"},"schema_version":"1.0","source":{"id":"1210.1715","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.1715","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"arxiv_version","alias_value":"1210.1715v2","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1715","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"pith_short_12","alias_value":"GZCDQCMTYOXP","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GZCDQCMTYOXPTQAJ","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GZCDQCMT","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:e5755b8934b37710b128ec1cee3a842148ae3ba0ef7be168ad618fdf647182e0","target":"graph","created_at":"2026-05-18T03:20:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We address the problem of adaptive minimax density estimation on $\\bR^d$ with $\\bL_p$--loss on the anisotropic Nikol'skii classes. We fully characterize behavior of the minimax risk for different relationships between regularity parameters and norm indexes in definitions of the functional class and of the risk. In particular, we show that there are four different regimes with respect to the behavior of the minimax risk. We develop a single estimator which is (nearly) optimal in orderover the complete scale of the anisotropic Nikol'skii classes. Our estimation procedure is based on a data-drive","authors_text":"A. Goldenshluger, O. Lepski","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-10-05T11:36:43Z","title":"On adaptive minimax density estimation on $R^d$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1715","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d1716633a9858bd4181cb28c6444c40c1a3746259e17e42ab1a74767e7277c5d","target":"record","created_at":"2026-05-18T03:20:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"08ee6f5211f44510b9e68653d8b80ce2d3d15d01666dc4d1d8cd0b2185d198ff","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-10-05T11:36:43Z","title_canon_sha256":"224309ee136d50af512b3542870f067f3114904aad54c61d7d9415f9a42ce6a7"},"schema_version":"1.0","source":{"id":"1210.1715","kind":"arxiv","version":2}},"canonical_sha256":"3644380993c3aef9c0097f6b571264c5fb99b59ede2d31ff84fa7303aecc847d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3644380993c3aef9c0097f6b571264c5fb99b59ede2d31ff84fa7303aecc847d","first_computed_at":"2026-05-18T03:20:45.346083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:45.346083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WckfdqqhQX5MuMfO+yUYUVjG9h0QbqPCSzkXoVIa2Rwb9PhH8k4pz6QS1Gu3j4mBOAhjLk9YRefM6i1cttnRDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:45.346738Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.1715","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1716633a9858bd4181cb28c6444c40c1a3746259e17e42ab1a74767e7277c5d","sha256:e5755b8934b37710b128ec1cee3a842148ae3ba0ef7be168ad618fdf647182e0"],"state_sha256":"59100bbf5ebb8ddceea00b6aa26e81b6678f2bb125a3e7d71152c9f39160529c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UjAdtQ2kbxqB46QX1Q10YFQ6F/6n2Dw6JoBanJPj4DvjWBPBTDBzrm+DA+l6828c+5a7inXRqWF+YjVSeR5GBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T12:51:28.242666Z","bundle_sha256":"ad1108d8815f7c9b8637e1b6eee36e8b6b867c353e71c16d4c5e96bf78ea10b0"}}