{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:E3YGVIQS5XSEUTDZSBSTZO67J7","short_pith_number":"pith:E3YGVIQS","canonical_record":{"source":{"id":"1506.02166","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-06-06T15:53:11Z","cross_cats_sorted":[],"title_canon_sha256":"677510c8f37ba9495cff342756fa328300483fe48fe02e9a3e9bf99ed41e638d","abstract_canon_sha256":"1bc79eb6d4e1dd72dc506b0bf140dc1387f84aeb83d0d8f524b19c92bf38a3b2"},"schema_version":"1.0"},"canonical_sha256":"26f06aa212ede44a4c7990653cbbdf4fd5ccec4c3cf5482f49379552e927e4b2","source":{"kind":"arxiv","id":"1506.02166","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02166","created_at":"2026-05-18T01:30:34Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02166v2","created_at":"2026-05-18T01:30:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02166","created_at":"2026-05-18T01:30:34Z"},{"alias_kind":"pith_short_12","alias_value":"E3YGVIQS5XSE","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"E3YGVIQS5XSEUTDZ","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"E3YGVIQS","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:E3YGVIQS5XSEUTDZSBSTZO67J7","target":"record","payload":{"canonical_record":{"source":{"id":"1506.02166","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-06-06T15:53:11Z","cross_cats_sorted":[],"title_canon_sha256":"677510c8f37ba9495cff342756fa328300483fe48fe02e9a3e9bf99ed41e638d","abstract_canon_sha256":"1bc79eb6d4e1dd72dc506b0bf140dc1387f84aeb83d0d8f524b19c92bf38a3b2"},"schema_version":"1.0"},"canonical_sha256":"26f06aa212ede44a4c7990653cbbdf4fd5ccec4c3cf5482f49379552e927e4b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:34.472870Z","signature_b64":"mdBYSAw0FoWKI7u04x6U0ZyQQCvhTWHNzwk5Dr2n8ZnxGGX8POgCVAxV+2Op/JwDqEjDeWauN8pkO4+geK9DCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26f06aa212ede44a4c7990653cbbdf4fd5ccec4c3cf5482f49379552e927e4b2","last_reissued_at":"2026-05-18T01:30:34.472200Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:34.472200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.02166","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":"2026-05-18T01:30:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gatosKQ4cga68Sb0zQIu+oG+X+nFgouWE8lh4+Bpu9iAXpegvTQyLiurf6/04NG6JLnn/WuWPBPlG4am9khgCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T02:12:17.776945Z"},"content_sha256":"2dbbf9f162e4af039616e67ecc3d8d5152a3e2a8968360729045455f9fbde23b","schema_version":"1.0","event_id":"sha256:2dbbf9f162e4af039616e67ecc3d8d5152a3e2a8968360729045455f9fbde23b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:E3YGVIQS5XSEUTDZSBSTZO67J7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards a better understanding of the dual representation of phi divergences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Diaa Al Mohamad","submitted_at":"2015-06-06T15:53:11Z","abstract_excerpt":"The aim of this paper is to study different estimation procedures based on $\\varphi-$divergences. The dual representation of $\\varphi-$divergences based on the Fenchel-Legendre duality is the main interest of this study. It provides a way to estimate $\\varphi-$divergences by a simple plug-in of the empirical distribution without any smoothing technique. Resulting estimators are thoroughly studied theoretically and with simulations showing that the so called minimum $\\varphi-$divergence estimator (MD$\\varphi$DE) is generally non robust and behaves similarly to the maximum likelihood estimator. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02166","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":"2026-05-18T01:30:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EDfK013YTLfJXV/9iY9rt7laBSEsHA+KF0aAG50AkUas4fYzxftkg3oqjLNhwNCQ4LwTsm5+n4pzQwaykTlbBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T02:12:17.777292Z"},"content_sha256":"31992f176167e4d89f823e787c578a331fc56e0f3a95f21219be0de4b00430f3","schema_version":"1.0","event_id":"sha256:31992f176167e4d89f823e787c578a331fc56e0f3a95f21219be0de4b00430f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E3YGVIQS5XSEUTDZSBSTZO67J7/bundle.json","state_url":"https://pith.science/pith/E3YGVIQS5XSEUTDZSBSTZO67J7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E3YGVIQS5XSEUTDZSBSTZO67J7/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":"2026-06-22T02:12:17Z","links":{"resolver":"https://pith.science/pith/E3YGVIQS5XSEUTDZSBSTZO67J7","bundle":"https://pith.science/pith/E3YGVIQS5XSEUTDZSBSTZO67J7/bundle.json","state":"https://pith.science/pith/E3YGVIQS5XSEUTDZSBSTZO67J7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E3YGVIQS5XSEUTDZSBSTZO67J7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:E3YGVIQS5XSEUTDZSBSTZO67J7","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":"1bc79eb6d4e1dd72dc506b0bf140dc1387f84aeb83d0d8f524b19c92bf38a3b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-06-06T15:53:11Z","title_canon_sha256":"677510c8f37ba9495cff342756fa328300483fe48fe02e9a3e9bf99ed41e638d"},"schema_version":"1.0","source":{"id":"1506.02166","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02166","created_at":"2026-05-18T01:30:34Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02166v2","created_at":"2026-05-18T01:30:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02166","created_at":"2026-05-18T01:30:34Z"},{"alias_kind":"pith_short_12","alias_value":"E3YGVIQS5XSE","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"E3YGVIQS5XSEUTDZ","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"E3YGVIQS","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:31992f176167e4d89f823e787c578a331fc56e0f3a95f21219be0de4b00430f3","target":"graph","created_at":"2026-05-18T01:30:34Z","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":"The aim of this paper is to study different estimation procedures based on $\\varphi-$divergences. The dual representation of $\\varphi-$divergences based on the Fenchel-Legendre duality is the main interest of this study. It provides a way to estimate $\\varphi-$divergences by a simple plug-in of the empirical distribution without any smoothing technique. Resulting estimators are thoroughly studied theoretically and with simulations showing that the so called minimum $\\varphi-$divergence estimator (MD$\\varphi$DE) is generally non robust and behaves similarly to the maximum likelihood estimator. ","authors_text":"Diaa Al Mohamad","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-06-06T15:53:11Z","title":"Towards a better understanding of the dual representation of phi divergences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02166","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":"sha256:2dbbf9f162e4af039616e67ecc3d8d5152a3e2a8968360729045455f9fbde23b","target":"record","created_at":"2026-05-18T01:30:34Z","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":"1bc79eb6d4e1dd72dc506b0bf140dc1387f84aeb83d0d8f524b19c92bf38a3b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-06-06T15:53:11Z","title_canon_sha256":"677510c8f37ba9495cff342756fa328300483fe48fe02e9a3e9bf99ed41e638d"},"schema_version":"1.0","source":{"id":"1506.02166","kind":"arxiv","version":2}},"canonical_sha256":"26f06aa212ede44a4c7990653cbbdf4fd5ccec4c3cf5482f49379552e927e4b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26f06aa212ede44a4c7990653cbbdf4fd5ccec4c3cf5482f49379552e927e4b2","first_computed_at":"2026-05-18T01:30:34.472200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:34.472200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mdBYSAw0FoWKI7u04x6U0ZyQQCvhTWHNzwk5Dr2n8ZnxGGX8POgCVAxV+2Op/JwDqEjDeWauN8pkO4+geK9DCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:34.472870Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02166","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2dbbf9f162e4af039616e67ecc3d8d5152a3e2a8968360729045455f9fbde23b","sha256:31992f176167e4d89f823e787c578a331fc56e0f3a95f21219be0de4b00430f3"],"state_sha256":"95781116aeacacb4f3b3cf97b31278f56721551ab95b8b8e4fc474b7c41665c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xqBG+q0hBNQf2bgVS9eQwzTwKnqCpDZOpT+MZdASlYNO5yzCRvq77kCweuCORo2PQeCSv1JpT41kMeObskrMCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T02:12:17.779181Z","bundle_sha256":"2af8aef2c866aa8d92463834113f67ea1fa3bf1e327404f08f0fc61174826fb0"}}