{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LKPIP6XITA4CG5RI3CLDP4U44C","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":"17e8ea47c1e7c476edd7a0019821a788aa84fb5a4201cd84055171e836587f15","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-03-06T07:06:54Z","title_canon_sha256":"265d5ebdbdcb97e8b6e84ac04ca3edaea89faf811b0d3ea896084d0a87c114bd"},"schema_version":"1.0","source":{"id":"1203.1112","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1112","created_at":"2026-05-18T02:56:35Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1112v4","created_at":"2026-05-18T02:56:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1112","created_at":"2026-05-18T02:56:35Z"},{"alias_kind":"pith_short_12","alias_value":"LKPIP6XITA4C","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LKPIP6XITA4CG5RI","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LKPIP6XI","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:418dd787b3a3345d3f1ed8e78201a2497a116b1a8ac80a6fd8a72bf0528587fa","target":"graph","created_at":"2026-05-18T02:56:35Z","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":"We derive a new representation for $U$- and $V$-statistics. Using this representation, the asymptotic distribution of $U$- and $V$-statistics can be derived by a direct application of the Continuous Mapping theorem. That novel approach not only encompasses most of the results on the asymptotic distribution known in literature, but also allows for the first time a unifying treatment of non-degenerate and degenerate $U$- and $V$-statistics. Moreover, it yields a new and powerful tool to derive the asymptotic distribution of very general $U$- and $V$-statistics based on long-memory sequences. Thi","authors_text":"Eric Beutner, Henryk Z\\\"ahle","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-03-06T07:06:54Z","title":"Continuous mapping approach to the asymptotics of $U$- and $V$-statistics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1112","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":"sha256:19a5f578f85edbd653664866a4cd287ce7ae41c5436d8fd29004931156582c5d","target":"record","created_at":"2026-05-18T02:56:35Z","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":"17e8ea47c1e7c476edd7a0019821a788aa84fb5a4201cd84055171e836587f15","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-03-06T07:06:54Z","title_canon_sha256":"265d5ebdbdcb97e8b6e84ac04ca3edaea89faf811b0d3ea896084d0a87c114bd"},"schema_version":"1.0","source":{"id":"1203.1112","kind":"arxiv","version":4}},"canonical_sha256":"5a9e87fae89838237628d89637f29ce0b566b2539edcd7b5806dd1ad572eca22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a9e87fae89838237628d89637f29ce0b566b2539edcd7b5806dd1ad572eca22","first_computed_at":"2026-05-18T02:56:35.572641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:35.572641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3a1OjKTsjvmOZYFSHHRUrnB+SUQFmYvuUJdfdKerPOX1ecrGmSIdpPkWrYRz45xnawDSGL2G95KsSIMJJly6BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:35.573392Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.1112","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19a5f578f85edbd653664866a4cd287ce7ae41c5436d8fd29004931156582c5d","sha256:418dd787b3a3345d3f1ed8e78201a2497a116b1a8ac80a6fd8a72bf0528587fa"],"state_sha256":"68683cfe20bd591f1af54c9441342871754b6479191286742b2247be9344100b"}