{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UXK32HBET7DXO2QOOX3EDKUKEH","short_pith_number":"pith:UXK32HBE","canonical_record":{"source":{"id":"1708.02705","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-09T03:43:03Z","cross_cats_sorted":["math.PR","stat.ME","stat.TH"],"title_canon_sha256":"46d0d3407911dd34fa554bcfb13969ebda0d09466b2832a1b3e30f17f2ae760f","abstract_canon_sha256":"bda9e501c7945fefb005560cfd5328fe56c33f98653c5ae06320dd63239294af"},"schema_version":"1.0"},"canonical_sha256":"a5d5bd1c249fc7776a0e75f641aa8a21c468cfa65c0ce60171b22f9f648c4300","source":{"kind":"arxiv","id":"1708.02705","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02705","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02705v4","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02705","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"pith_short_12","alias_value":"UXK32HBET7DX","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UXK32HBET7DXO2QO","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UXK32HBE","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UXK32HBET7DXO2QOOX3EDKUKEH","target":"record","payload":{"canonical_record":{"source":{"id":"1708.02705","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-09T03:43:03Z","cross_cats_sorted":["math.PR","stat.ME","stat.TH"],"title_canon_sha256":"46d0d3407911dd34fa554bcfb13969ebda0d09466b2832a1b3e30f17f2ae760f","abstract_canon_sha256":"bda9e501c7945fefb005560cfd5328fe56c33f98653c5ae06320dd63239294af"},"schema_version":"1.0"},"canonical_sha256":"a5d5bd1c249fc7776a0e75f641aa8a21c468cfa65c0ce60171b22f9f648c4300","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:03.265118Z","signature_b64":"ozJb1S7Luuu2p/FJqaXAV35BBrA6lY9YIItXcjmtbfHrt4fOT6LuNODJaYfSLOGthLEwz47cAPusf8Y4oBWfCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5d5bd1c249fc7776a0e75f641aa8a21c468cfa65c0ce60171b22f9f648c4300","last_reissued_at":"2026-05-17T23:54:03.264601Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:03.264601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.02705","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":"2026-05-17T23:54:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vFsMzo7F8UMX9TYZ+i6c3ioogEVxmJ+BNHKNLmkx73JAGqMe3cdt+4fEp7rxOtsGpYxS5wsWIsnoVqHKtuCxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T08:22:24.778617Z"},"content_sha256":"daf0912f9c2655e164a49b29b037fd036c52d340cb1695ce9c18eec4eee2c564","schema_version":"1.0","event_id":"sha256:daf0912f9c2655e164a49b29b037fd036c52d340cb1695ce9c18eec4eee2c564"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UXK32HBET7DXO2QOOX3EDKUKEH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Jackknife multiplier bootstrap: finite sample approximations to the $U$-process supremum with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Kengo Kato, Xiaohui Chen","submitted_at":"2017-08-09T03:43:03Z","abstract_excerpt":"This paper is concerned with finite sample approximations to the supremum of a non-degenerate $U$-process of a general order indexed by a function class. We are primarily interested in situations where the function class as well as the underlying distribution change with the sample size, and the $U$-process itself is not weakly convergent as a process. Such situations arise in a variety of modern statistical problems. We first consider Gaussian approximations, namely, approximate the $U$-process supremum by the supremum of a Gaussian process, and derive coupling and Kolmogorov distance bounds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02705","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":"2026-05-17T23:54:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bQ6XwCWb8RvZ1X4qvSlQCrRa6hAFH5zWHPM2gr9k5G66cxKutrP2aAngqj1ZJBITY1ZYNLrsz5daThSqu3e8CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T08:22:24.779303Z"},"content_sha256":"b4a631da75eee1562a17248f856640cd657e8dd20b2960971a08b6d4f34c472f","schema_version":"1.0","event_id":"sha256:b4a631da75eee1562a17248f856640cd657e8dd20b2960971a08b6d4f34c472f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UXK32HBET7DXO2QOOX3EDKUKEH/bundle.json","state_url":"https://pith.science/pith/UXK32HBET7DXO2QOOX3EDKUKEH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UXK32HBET7DXO2QOOX3EDKUKEH/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":"2026-05-25T08:22:24Z","links":{"resolver":"https://pith.science/pith/UXK32HBET7DXO2QOOX3EDKUKEH","bundle":"https://pith.science/pith/UXK32HBET7DXO2QOOX3EDKUKEH/bundle.json","state":"https://pith.science/pith/UXK32HBET7DXO2QOOX3EDKUKEH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UXK32HBET7DXO2QOOX3EDKUKEH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UXK32HBET7DXO2QOOX3EDKUKEH","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":"bda9e501c7945fefb005560cfd5328fe56c33f98653c5ae06320dd63239294af","cross_cats_sorted":["math.PR","stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-09T03:43:03Z","title_canon_sha256":"46d0d3407911dd34fa554bcfb13969ebda0d09466b2832a1b3e30f17f2ae760f"},"schema_version":"1.0","source":{"id":"1708.02705","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02705","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02705v4","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02705","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"pith_short_12","alias_value":"UXK32HBET7DX","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UXK32HBET7DXO2QO","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UXK32HBE","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:b4a631da75eee1562a17248f856640cd657e8dd20b2960971a08b6d4f34c472f","target":"graph","created_at":"2026-05-17T23:54:03Z","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":"This paper is concerned with finite sample approximations to the supremum of a non-degenerate $U$-process of a general order indexed by a function class. We are primarily interested in situations where the function class as well as the underlying distribution change with the sample size, and the $U$-process itself is not weakly convergent as a process. Such situations arise in a variety of modern statistical problems. We first consider Gaussian approximations, namely, approximate the $U$-process supremum by the supremum of a Gaussian process, and derive coupling and Kolmogorov distance bounds.","authors_text":"Kengo Kato, Xiaohui Chen","cross_cats":["math.PR","stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-09T03:43:03Z","title":"Jackknife multiplier bootstrap: finite sample approximations to the $U$-process supremum with applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02705","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:daf0912f9c2655e164a49b29b037fd036c52d340cb1695ce9c18eec4eee2c564","target":"record","created_at":"2026-05-17T23:54:03Z","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":"bda9e501c7945fefb005560cfd5328fe56c33f98653c5ae06320dd63239294af","cross_cats_sorted":["math.PR","stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-09T03:43:03Z","title_canon_sha256":"46d0d3407911dd34fa554bcfb13969ebda0d09466b2832a1b3e30f17f2ae760f"},"schema_version":"1.0","source":{"id":"1708.02705","kind":"arxiv","version":4}},"canonical_sha256":"a5d5bd1c249fc7776a0e75f641aa8a21c468cfa65c0ce60171b22f9f648c4300","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5d5bd1c249fc7776a0e75f641aa8a21c468cfa65c0ce60171b22f9f648c4300","first_computed_at":"2026-05-17T23:54:03.264601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:03.264601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ozJb1S7Luuu2p/FJqaXAV35BBrA6lY9YIItXcjmtbfHrt4fOT6LuNODJaYfSLOGthLEwz47cAPusf8Y4oBWfCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:03.265118Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.02705","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:daf0912f9c2655e164a49b29b037fd036c52d340cb1695ce9c18eec4eee2c564","sha256:b4a631da75eee1562a17248f856640cd657e8dd20b2960971a08b6d4f34c472f"],"state_sha256":"0ef1752fe4dc82db8a033e2f495c3eaf9c1dc9a3567167d6c0cd3c743df67037"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FpVv1tYw+fUAuQ6elDZthBozYkQ7H8WnkrdJiS97aE85vxr+KEPv8z7Hp846duC3yuj2b0A4qnYBYNcgMkeYBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T08:22:24.783552Z","bundle_sha256":"a51fa24dab21bb659eff31970db2e2d22d2e32e8e79e4557c27e62d10ee3d3b6"}}