{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UUQ7AGZZA5L4ZGTMX4AKY372D7","short_pith_number":"pith:UUQ7AGZZ","canonical_record":{"source":{"id":"1710.09072","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-25T04:36:53Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"b0e486f4cbc215d43940aac84ab2400897d009a15fd85412456d88000a0269d4","abstract_canon_sha256":"8efde2b0de0e737b5d2ee03fd77ad564534609af436f75437fada2351d4c58a4"},"schema_version":"1.0"},"canonical_sha256":"a521f01b390757cc9a6cbf00ac6ffa1fccc08a339e0cccf451443d8ab329e66f","source":{"kind":"arxiv","id":"1710.09072","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.09072","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"arxiv_version","alias_value":"1710.09072v4","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09072","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"pith_short_12","alias_value":"UUQ7AGZZA5L4","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UUQ7AGZZA5L4ZGTM","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UUQ7AGZZ","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UUQ7AGZZA5L4ZGTMX4AKY372D7","target":"record","payload":{"canonical_record":{"source":{"id":"1710.09072","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-25T04:36:53Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"b0e486f4cbc215d43940aac84ab2400897d009a15fd85412456d88000a0269d4","abstract_canon_sha256":"8efde2b0de0e737b5d2ee03fd77ad564534609af436f75437fada2351d4c58a4"},"schema_version":"1.0"},"canonical_sha256":"a521f01b390757cc9a6cbf00ac6ffa1fccc08a339e0cccf451443d8ab329e66f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:18.805481Z","signature_b64":"bFn6p2c5Yn9soUxGaG6Ip816zzSd3Ps/oQCwOhDCUD8WMzwo7zWsDrMTTefA1JSpqJjcqzCfcXzAzosB3PZ5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a521f01b390757cc9a6cbf00ac6ffa1fccc08a339e0cccf451443d8ab329e66f","last_reissued_at":"2026-05-17T23:52:18.804719Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:18.804719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.09072","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B3w8rIJWOhxXU6glqz89jIa+czitJl3cLUPoU54Eck/cWXVNkesDACzF8TPGGfpu9E8g1ayKX+47jJtzLywIDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T05:44:01.170744Z"},"content_sha256":"1bfb4bc45f14dc6140d560655c1dee93307d6ee7595edccfcb318c4b5aaf555d","schema_version":"1.0","event_id":"sha256:1bfb4bc45f14dc6140d560655c1dee93307d6ee7595edccfcb318c4b5aaf555d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UUQ7AGZZA5L4ZGTMX4AKY372D7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotically Efficient Estimation of Smooth Functionals of Covariance Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Vladimir Koltchinskii","submitted_at":"2017-10-25T04:36:53Z","abstract_excerpt":"Let $X$ be a centered Gaussian random variable in a separable Hilbert space ${\\mathbb H}$ with covariance operator $\\Sigma.$ We study a problem of estimation of a smooth functional of $\\Sigma$ based on a sample $X_1,\\dots ,X_n$ of $n$ independent observations of $X.$ More specifically, we are interested in functionals of the form $\\langle f(\\Sigma), B\\rangle,$ where $f:{\\mathbb R}\\mapsto {\\mathbb R}$ is a smooth function and $B$ is a nuclear operator in ${\\mathbb H}.$ We prove concentration and normal approximation bounds for plug-in estimator $\\langle f(\\hat \\Sigma),B\\rangle,$ $\\hat \\Sigma:=n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09072","kind":"arxiv","version":4},"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":"2026-05-17T23:52:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pkxPsaKRzmF/oEDDYkV3opKXNQTeTtZq0WXB8hQwYTnZC+1pgXbQ0kvlOrYIbKfS8m5DVa8OCV/3J83wVCVVDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T05:44:01.171347Z"},"content_sha256":"2579a4b64016b24e21e6591241c66bb6a7739f2dbb06509eb8cfe038f6b654e7","schema_version":"1.0","event_id":"sha256:2579a4b64016b24e21e6591241c66bb6a7739f2dbb06509eb8cfe038f6b654e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UUQ7AGZZA5L4ZGTMX4AKY372D7/bundle.json","state_url":"https://pith.science/pith/UUQ7AGZZA5L4ZGTMX4AKY372D7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UUQ7AGZZA5L4ZGTMX4AKY372D7/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":"2026-07-04T05:44:01Z","links":{"resolver":"https://pith.science/pith/UUQ7AGZZA5L4ZGTMX4AKY372D7","bundle":"https://pith.science/pith/UUQ7AGZZA5L4ZGTMX4AKY372D7/bundle.json","state":"https://pith.science/pith/UUQ7AGZZA5L4ZGTMX4AKY372D7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UUQ7AGZZA5L4ZGTMX4AKY372D7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UUQ7AGZZA5L4ZGTMX4AKY372D7","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":"8efde2b0de0e737b5d2ee03fd77ad564534609af436f75437fada2351d4c58a4","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-25T04:36:53Z","title_canon_sha256":"b0e486f4cbc215d43940aac84ab2400897d009a15fd85412456d88000a0269d4"},"schema_version":"1.0","source":{"id":"1710.09072","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.09072","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"arxiv_version","alias_value":"1710.09072v4","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09072","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"pith_short_12","alias_value":"UUQ7AGZZA5L4","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UUQ7AGZZA5L4ZGTM","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UUQ7AGZZ","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:2579a4b64016b24e21e6591241c66bb6a7739f2dbb06509eb8cfe038f6b654e7","target":"graph","created_at":"2026-05-17T23:52:18Z","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":"Let $X$ be a centered Gaussian random variable in a separable Hilbert space ${\\mathbb H}$ with covariance operator $\\Sigma.$ We study a problem of estimation of a smooth functional of $\\Sigma$ based on a sample $X_1,\\dots ,X_n$ of $n$ independent observations of $X.$ More specifically, we are interested in functionals of the form $\\langle f(\\Sigma), B\\rangle,$ where $f:{\\mathbb R}\\mapsto {\\mathbb R}$ is a smooth function and $B$ is a nuclear operator in ${\\mathbb H}.$ We prove concentration and normal approximation bounds for plug-in estimator $\\langle f(\\hat \\Sigma),B\\rangle,$ $\\hat \\Sigma:=n","authors_text":"Vladimir Koltchinskii","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-25T04:36:53Z","title":"Asymptotically Efficient Estimation of Smooth Functionals of Covariance Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09072","kind":"arxiv","version":4},"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":"sha256:1bfb4bc45f14dc6140d560655c1dee93307d6ee7595edccfcb318c4b5aaf555d","target":"record","created_at":"2026-05-17T23:52:18Z","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":"8efde2b0de0e737b5d2ee03fd77ad564534609af436f75437fada2351d4c58a4","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-25T04:36:53Z","title_canon_sha256":"b0e486f4cbc215d43940aac84ab2400897d009a15fd85412456d88000a0269d4"},"schema_version":"1.0","source":{"id":"1710.09072","kind":"arxiv","version":4}},"canonical_sha256":"a521f01b390757cc9a6cbf00ac6ffa1fccc08a339e0cccf451443d8ab329e66f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a521f01b390757cc9a6cbf00ac6ffa1fccc08a339e0cccf451443d8ab329e66f","first_computed_at":"2026-05-17T23:52:18.804719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:18.804719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bFn6p2c5Yn9soUxGaG6Ip816zzSd3Ps/oQCwOhDCUD8WMzwo7zWsDrMTTefA1JSpqJjcqzCfcXzAzosB3PZ5Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:18.805481Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.09072","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bfb4bc45f14dc6140d560655c1dee93307d6ee7595edccfcb318c4b5aaf555d","sha256:2579a4b64016b24e21e6591241c66bb6a7739f2dbb06509eb8cfe038f6b654e7"],"state_sha256":"9e12259a707afc40cf43ecf8f492e993a9624dcecb0aa2523c773e35c35284b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gimZOwnIqEB5rRtHmit8P4+9avX532yDJdeER7wjK7a/XPGMkyFLLQN3ig2y79/Xckv/WpeKP+ryCy7J5aKvCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T05:44:01.174566Z","bundle_sha256":"31f0ba861489356cae0839eb15cb5484f99211b0b8918ee0aab86eccbd9fdb67"}}