{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:IFDORI4U3Z5MQIPUFGO5ND65YI","short_pith_number":"pith:IFDORI4U","schema_version":"1.0","canonical_sha256":"4146e8a394de7ac821f4299dd68fddc2177d3bec2510a32400140a88d1de0079","source":{"kind":"arxiv","id":"1711.10649","version":2},"attestation_state":"computed","paper":{"title":"Limit theorems with rate of convergence under sublinear expectations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Qi-Man Shao, Shige Peng, Xiao Fang, Yongsheng Song","submitted_at":"2017-11-29T02:32:10Z","abstract_excerpt":"Under the sublinear expectation $\\mathbb{E}[\\cdot]:=\\sup_{\\theta\\in \\Theta} E_\\theta[\\cdot]$ for a given set of linear expectations $\\{E_\\theta: \\theta\\in \\Theta\\}$, we establish a new law of large numbers and a new central limit theorem with rate of convergence. We present some interesting special cases and discuss a related statistical inference problem. We also give an approximation and a representation of the $G$-normal distribution, which was used as the limit in Peng (2007)'s central limit theorem, in a probability space."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1711.10649","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-29T02:32:10Z","cross_cats_sorted":[],"title_canon_sha256":"72c976b204459cd073eaaf01e777fc5e9566efaeb139b9cf970bd247da8797dd","abstract_canon_sha256":"8a85a09a4e1e70adc9ea630011c7054db3fad45752bf0753e70dbd7b40e4a86e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:58.560559Z","signature_b64":"hCoCyvUXg0pOTHZtcasJLYBLCWcZNBCZIMeBJaBwWL2E5wnOnCE5B+N8JiM4YlxUD/bnRr4fc8I4bsfAWKcyCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4146e8a394de7ac821f4299dd68fddc2177d3bec2510a32400140a88d1de0079","last_reissued_at":"2026-05-18T00:15:58.559818Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:58.559818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Limit theorems with rate of convergence under sublinear expectations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Qi-Man Shao, Shige Peng, Xiao Fang, Yongsheng Song","submitted_at":"2017-11-29T02:32:10Z","abstract_excerpt":"Under the sublinear expectation $\\mathbb{E}[\\cdot]:=\\sup_{\\theta\\in \\Theta} E_\\theta[\\cdot]$ for a given set of linear expectations $\\{E_\\theta: \\theta\\in \\Theta\\}$, we establish a new law of large numbers and a new central limit theorem with rate of convergence. We present some interesting special cases and discuss a related statistical inference problem. We also give an approximation and a representation of the $G$-normal distribution, which was used as the limit in Peng (2007)'s central limit theorem, in a probability space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10649","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1711.10649","created_at":"2026-05-18T00:15:58.559933+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.10649v2","created_at":"2026-05-18T00:15:58.559933+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10649","created_at":"2026-05-18T00:15:58.559933+00:00"},{"alias_kind":"pith_short_12","alias_value":"IFDORI4U3Z5M","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"IFDORI4U3Z5MQIPU","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"IFDORI4U","created_at":"2026-05-18T12:31:21.493067+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IFDORI4U3Z5MQIPUFGO5ND65YI","json":"https://pith.science/pith/IFDORI4U3Z5MQIPUFGO5ND65YI.json","graph_json":"https://pith.science/api/pith-number/IFDORI4U3Z5MQIPUFGO5ND65YI/graph.json","events_json":"https://pith.science/api/pith-number/IFDORI4U3Z5MQIPUFGO5ND65YI/events.json","paper":"https://pith.science/paper/IFDORI4U"},"agent_actions":{"view_html":"https://pith.science/pith/IFDORI4U3Z5MQIPUFGO5ND65YI","download_json":"https://pith.science/pith/IFDORI4U3Z5MQIPUFGO5ND65YI.json","view_paper":"https://pith.science/paper/IFDORI4U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.10649&json=true","fetch_graph":"https://pith.science/api/pith-number/IFDORI4U3Z5MQIPUFGO5ND65YI/graph.json","fetch_events":"https://pith.science/api/pith-number/IFDORI4U3Z5MQIPUFGO5ND65YI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IFDORI4U3Z5MQIPUFGO5ND65YI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IFDORI4U3Z5MQIPUFGO5ND65YI/action/storage_attestation","attest_author":"https://pith.science/pith/IFDORI4U3Z5MQIPUFGO5ND65YI/action/author_attestation","sign_citation":"https://pith.science/pith/IFDORI4U3Z5MQIPUFGO5ND65YI/action/citation_signature","submit_replication":"https://pith.science/pith/IFDORI4U3Z5MQIPUFGO5ND65YI/action/replication_record"}},"created_at":"2026-05-18T00:15:58.559933+00:00","updated_at":"2026-05-18T00:15:58.559933+00:00"}