{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:T3QSLLWZAJJ7TMG7GGABUFJAA3","short_pith_number":"pith:T3QSLLWZ","canonical_record":{"source":{"id":"1612.09004","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-12-28T23:16:27Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"456f9afe949a06b4fbcc54423e56b877bf9d19a03d860d039f3dfec769ea9b3e","abstract_canon_sha256":"028db1db193a57aaf4d74f9970d8752956db93c6d403551625ec1dad2d2f78b7"},"schema_version":"1.0"},"canonical_sha256":"9ee125aed90253f9b0df31801a152006ef9fee06a9876d9ffba2886edd7eb68a","source":{"kind":"arxiv","id":"1612.09004","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09004","created_at":"2026-05-18T00:53:46Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09004v1","created_at":"2026-05-18T00:53:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09004","created_at":"2026-05-18T00:53:46Z"},{"alias_kind":"pith_short_12","alias_value":"T3QSLLWZAJJ7","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"T3QSLLWZAJJ7TMG7","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"T3QSLLWZ","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:T3QSLLWZAJJ7TMG7GGABUFJAA3","target":"record","payload":{"canonical_record":{"source":{"id":"1612.09004","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-12-28T23:16:27Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"456f9afe949a06b4fbcc54423e56b877bf9d19a03d860d039f3dfec769ea9b3e","abstract_canon_sha256":"028db1db193a57aaf4d74f9970d8752956db93c6d403551625ec1dad2d2f78b7"},"schema_version":"1.0"},"canonical_sha256":"9ee125aed90253f9b0df31801a152006ef9fee06a9876d9ffba2886edd7eb68a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:46.659675Z","signature_b64":"ZgRI0xsa8N6QEoZGRyBktScJOwwrwNkiOeCI24GqCHNhomg6PWov9IIr+b7HDvplz8Ui+mKO9ANRMJqLjkdBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ee125aed90253f9b0df31801a152006ef9fee06a9876d9ffba2886edd7eb68a","last_reissued_at":"2026-05-18T00:53:46.659078Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:46.659078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.09004","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fvzyOL2RDcYnEZ+c4qUrExzzX4i42e2Vz9ixoU5G1mHadJk1Pqc2Q3y2HFUHHozD/MY4+TAUrxk9bsdRfmEqAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T14:37:20.651071Z"},"content_sha256":"806007c9c93d2e7d9794f2413dcf2b362cbff0a470b2f70ca6617579dcc74a29","schema_version":"1.0","event_id":"sha256:806007c9c93d2e7d9794f2413dcf2b362cbff0a470b2f70ca6617579dcc74a29"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:T3QSLLWZAJJ7TMG7GGABUFJAA3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform in bandwidth consistency for the transformation kernel estimator of copulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Cheikh Tidiane Seck, Diam Ba, Gane Samb Lo","submitted_at":"2016-12-28T23:16:27Z","abstract_excerpt":"In this paper we establish the uniform in bandwidth consistency for the transformation kernel estimator of copulas introduced in [Omelka et al.(2009)]. To this end, we first prove a uniform in bandwidth law of the iterated logarithm for the maximal deviation of this estimator from its expectation. We then show that, as n goes to infinity, the bias of the estimator converges to zero uniformly in the bandwidth h, varying over a suitable interval. A practical method of selecting the optimal bandwidth is also presented. Finally, we make conclusive simulation experiments showing the performance of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09004","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"icvgySFQXtrf7yMchTOu+8svaw/XLDQ1rpj6Hh1Ktfj2n3oeUA0k/D1j6G6UOY/ElT2KL5dwoq32CA626TCxDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T14:37:20.651443Z"},"content_sha256":"6c95dff834ca1cfee9d6f92242e279d4ba77c9c759a07168dae57a0b6daf1135","schema_version":"1.0","event_id":"sha256:6c95dff834ca1cfee9d6f92242e279d4ba77c9c759a07168dae57a0b6daf1135"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T3QSLLWZAJJ7TMG7GGABUFJAA3/bundle.json","state_url":"https://pith.science/pith/T3QSLLWZAJJ7TMG7GGABUFJAA3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T3QSLLWZAJJ7TMG7GGABUFJAA3/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":"2026-06-25T14:37:20Z","links":{"resolver":"https://pith.science/pith/T3QSLLWZAJJ7TMG7GGABUFJAA3","bundle":"https://pith.science/pith/T3QSLLWZAJJ7TMG7GGABUFJAA3/bundle.json","state":"https://pith.science/pith/T3QSLLWZAJJ7TMG7GGABUFJAA3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T3QSLLWZAJJ7TMG7GGABUFJAA3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:T3QSLLWZAJJ7TMG7GGABUFJAA3","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":"028db1db193a57aaf4d74f9970d8752956db93c6d403551625ec1dad2d2f78b7","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-12-28T23:16:27Z","title_canon_sha256":"456f9afe949a06b4fbcc54423e56b877bf9d19a03d860d039f3dfec769ea9b3e"},"schema_version":"1.0","source":{"id":"1612.09004","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09004","created_at":"2026-05-18T00:53:46Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09004v1","created_at":"2026-05-18T00:53:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09004","created_at":"2026-05-18T00:53:46Z"},{"alias_kind":"pith_short_12","alias_value":"T3QSLLWZAJJ7","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"T3QSLLWZAJJ7TMG7","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"T3QSLLWZ","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:6c95dff834ca1cfee9d6f92242e279d4ba77c9c759a07168dae57a0b6daf1135","target":"graph","created_at":"2026-05-18T00:53:46Z","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":"In this paper we establish the uniform in bandwidth consistency for the transformation kernel estimator of copulas introduced in [Omelka et al.(2009)]. To this end, we first prove a uniform in bandwidth law of the iterated logarithm for the maximal deviation of this estimator from its expectation. We then show that, as n goes to infinity, the bias of the estimator converges to zero uniformly in the bandwidth h, varying over a suitable interval. A practical method of selecting the optimal bandwidth is also presented. Finally, we make conclusive simulation experiments showing the performance of ","authors_text":"Cheikh Tidiane Seck, Diam Ba, Gane Samb Lo","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-12-28T23:16:27Z","title":"Uniform in bandwidth consistency for the transformation kernel estimator of copulas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09004","kind":"arxiv","version":1},"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":"sha256:806007c9c93d2e7d9794f2413dcf2b362cbff0a470b2f70ca6617579dcc74a29","target":"record","created_at":"2026-05-18T00:53:46Z","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":"028db1db193a57aaf4d74f9970d8752956db93c6d403551625ec1dad2d2f78b7","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-12-28T23:16:27Z","title_canon_sha256":"456f9afe949a06b4fbcc54423e56b877bf9d19a03d860d039f3dfec769ea9b3e"},"schema_version":"1.0","source":{"id":"1612.09004","kind":"arxiv","version":1}},"canonical_sha256":"9ee125aed90253f9b0df31801a152006ef9fee06a9876d9ffba2886edd7eb68a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ee125aed90253f9b0df31801a152006ef9fee06a9876d9ffba2886edd7eb68a","first_computed_at":"2026-05-18T00:53:46.659078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:46.659078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZgRI0xsa8N6QEoZGRyBktScJOwwrwNkiOeCI24GqCHNhomg6PWov9IIr+b7HDvplz8Ui+mKO9ANRMJqLjkdBAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:46.659675Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.09004","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:806007c9c93d2e7d9794f2413dcf2b362cbff0a470b2f70ca6617579dcc74a29","sha256:6c95dff834ca1cfee9d6f92242e279d4ba77c9c759a07168dae57a0b6daf1135"],"state_sha256":"94b0d6e13fd508263db74ddb2fdc43eca1132f49f67f60ce837f4f70bc26d1d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ecPs77xCS4tMsnGXQXplLwmXVcYopsmSkViczCpqxq9JZpu8FyJAZC9xOwjmRcZJrZnSZcPsknGrPNzuHrD8Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T14:37:20.653462Z","bundle_sha256":"eff4ef7fede247aad79c553aa0f3a6b08c5fd5b694ff83becf45795a4f51d0c2"}}