{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:57WU3GUJFKRVSI3ECJD5CENRDL","short_pith_number":"pith:57WU3GUJ","canonical_record":{"source":{"id":"1304.3559","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-04-12T07:52:42Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"087699d46c7c903ae956d10aa061dcf802dc4c73f2783147a5f9a0915379959b","abstract_canon_sha256":"2f75f6bf440e1413ec3b342255c33a14f76db9cc06381b875197551b44413e71"},"schema_version":"1.0"},"canonical_sha256":"efed4d9a892aa35923641247d111b11ac123f555624436bde4aca9b47c989715","source":{"kind":"arxiv","id":"1304.3559","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.3559","created_at":"2026-05-18T03:28:07Z"},{"alias_kind":"arxiv_version","alias_value":"1304.3559v1","created_at":"2026-05-18T03:28:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3559","created_at":"2026-05-18T03:28:07Z"},{"alias_kind":"pith_short_12","alias_value":"57WU3GUJFKRV","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"57WU3GUJFKRVSI3E","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"57WU3GUJ","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:57WU3GUJFKRVSI3ECJD5CENRDL","target":"record","payload":{"canonical_record":{"source":{"id":"1304.3559","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-04-12T07:52:42Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"087699d46c7c903ae956d10aa061dcf802dc4c73f2783147a5f9a0915379959b","abstract_canon_sha256":"2f75f6bf440e1413ec3b342255c33a14f76db9cc06381b875197551b44413e71"},"schema_version":"1.0"},"canonical_sha256":"efed4d9a892aa35923641247d111b11ac123f555624436bde4aca9b47c989715","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:07.266372Z","signature_b64":"U7bT37sCpyGJYXmH+/RDGmN0tlHMYro2ECsksD9hUYsG8b2ZN9HlBXf2LS3utRVTjl5bjRz2fZ4A0t78BapEDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efed4d9a892aa35923641247d111b11ac123f555624436bde4aca9b47c989715","last_reissued_at":"2026-05-18T03:28:07.265630Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:07.265630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.3559","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":"2026-05-18T03:28:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yM2nhMnz9RiZFgpIgyOpmGkMGOF20cWMIfnXUTczL0+Crggx2MD8vxxSPYN62F1md+n4pat8s8mf3ZwXeOvkDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T14:10:24.275355Z"},"content_sha256":"1f277deab67dfc507324f3be53c8bf1bf5685b322356c5b3b607abe158a0c1a0","schema_version":"1.0","event_id":"sha256:1f277deab67dfc507324f3be53c8bf1bf5685b322356c5b3b607abe158a0c1a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:57WU3GUJFKRVSI3ECJD5CENRDL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sublinear expectation linear regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Lu Lin, Shuzhen Yang, Xin Wang, Yufeng Shi","submitted_at":"2013-04-12T07:52:42Z","abstract_excerpt":"Nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, especially in finance risk measure and management. Under the nonlinear expectation framework, however, the related statistical models and statistical inferences have not yet been well established. The goal of this paper is to construct the sublinear expectation regression and investigate its statistical inference. First, a sublinear expectation linear regression is defined and its identifiability is given. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3559","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":"2026-05-18T03:28:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sNDQc/mxgQPVR7K40E2cKLqiu8Yp/WJbZgtw5+Pqo9aOhi4G8tKWiCPfJ3SZjvlV5spgHxHEo86ZSo9/Hw6oCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T14:10:24.276056Z"},"content_sha256":"eb973a476ed131372628ff7d1af7f322742979d5f1b81bd6decf0cd4a2898e04","schema_version":"1.0","event_id":"sha256:eb973a476ed131372628ff7d1af7f322742979d5f1b81bd6decf0cd4a2898e04"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/57WU3GUJFKRVSI3ECJD5CENRDL/bundle.json","state_url":"https://pith.science/pith/57WU3GUJFKRVSI3ECJD5CENRDL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/57WU3GUJFKRVSI3ECJD5CENRDL/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":"2026-05-23T14:10:24Z","links":{"resolver":"https://pith.science/pith/57WU3GUJFKRVSI3ECJD5CENRDL","bundle":"https://pith.science/pith/57WU3GUJFKRVSI3ECJD5CENRDL/bundle.json","state":"https://pith.science/pith/57WU3GUJFKRVSI3ECJD5CENRDL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/57WU3GUJFKRVSI3ECJD5CENRDL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:57WU3GUJFKRVSI3ECJD5CENRDL","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":"2f75f6bf440e1413ec3b342255c33a14f76db9cc06381b875197551b44413e71","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-04-12T07:52:42Z","title_canon_sha256":"087699d46c7c903ae956d10aa061dcf802dc4c73f2783147a5f9a0915379959b"},"schema_version":"1.0","source":{"id":"1304.3559","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.3559","created_at":"2026-05-18T03:28:07Z"},{"alias_kind":"arxiv_version","alias_value":"1304.3559v1","created_at":"2026-05-18T03:28:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3559","created_at":"2026-05-18T03:28:07Z"},{"alias_kind":"pith_short_12","alias_value":"57WU3GUJFKRV","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"57WU3GUJFKRVSI3E","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"57WU3GUJ","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:eb973a476ed131372628ff7d1af7f322742979d5f1b81bd6decf0cd4a2898e04","target":"graph","created_at":"2026-05-18T03:28:07Z","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":"Nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, especially in finance risk measure and management. Under the nonlinear expectation framework, however, the related statistical models and statistical inferences have not yet been well established. The goal of this paper is to construct the sublinear expectation regression and investigate its statistical inference. First, a sublinear expectation linear regression is defined and its identifiability is given. Th","authors_text":"Lu Lin, Shuzhen Yang, Xin Wang, Yufeng Shi","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-04-12T07:52:42Z","title":"Sublinear expectation linear regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3559","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":"sha256:1f277deab67dfc507324f3be53c8bf1bf5685b322356c5b3b607abe158a0c1a0","target":"record","created_at":"2026-05-18T03:28:07Z","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":"2f75f6bf440e1413ec3b342255c33a14f76db9cc06381b875197551b44413e71","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-04-12T07:52:42Z","title_canon_sha256":"087699d46c7c903ae956d10aa061dcf802dc4c73f2783147a5f9a0915379959b"},"schema_version":"1.0","source":{"id":"1304.3559","kind":"arxiv","version":1}},"canonical_sha256":"efed4d9a892aa35923641247d111b11ac123f555624436bde4aca9b47c989715","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efed4d9a892aa35923641247d111b11ac123f555624436bde4aca9b47c989715","first_computed_at":"2026-05-18T03:28:07.265630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:07.265630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U7bT37sCpyGJYXmH+/RDGmN0tlHMYro2ECsksD9hUYsG8b2ZN9HlBXf2LS3utRVTjl5bjRz2fZ4A0t78BapEDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:07.266372Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.3559","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f277deab67dfc507324f3be53c8bf1bf5685b322356c5b3b607abe158a0c1a0","sha256:eb973a476ed131372628ff7d1af7f322742979d5f1b81bd6decf0cd4a2898e04"],"state_sha256":"4e29bcc2af68d9df9c4ebff1a83e6f34285c43a525b916df41a94b1ef5d015e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KzcQHmYVpY6diCQczosdtGDlQpbLCJCkL1i3pPTIPMcFb7hOZKblcs7KDdIU+mpWPAFq/qRt5wRCJkjaUu+jBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T14:10:24.279943Z","bundle_sha256":"fc27dadff54329a1d6444fbe8347451ee329c43aee0a93e49a9bb11647d39ca9"}}