{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CFI77ROO5QGOTOMXD3XJA2U5XB","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":"4efb286c69fe65f5b056e38a4820999d2116ee900642d65b960a337c5ce32b7f","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-05-25T03:03:02Z","title_canon_sha256":"29e62083926facf00aa0a49b26afd4f284f56c5d2e4c28e73e8bec9e1026bcb8"},"schema_version":"1.0","source":{"id":"1305.5882","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5882","created_at":"2026-05-18T03:21:42Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5882v2","created_at":"2026-05-18T03:21:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5882","created_at":"2026-05-18T03:21:42Z"},{"alias_kind":"pith_short_12","alias_value":"CFI77ROO5QGO","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CFI77ROO5QGOTOMX","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CFI77ROO","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:9eaee738d764be053a2cbe41196fc7df6476bbac038151cdc1261a7200a037ee","target":"graph","created_at":"2026-05-18T03:21:42Z","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":"In this paper, we construct a moment inequality for mixing dependent random variables, it is of independent interest. As applications, the consistency of the kernel density estimation is investigated. Several limit theorems are established: First, the central limit theorems for the kernel density estimator $f_{n,K}(x)$ and its distribution function are constructed. Also, the convergence rates of $\\|f_{n,K}(x)-Ef_{n,K}(x)\\|_{p}$ in sup-norm loss and integral $L^{p}$-norm loss are proved. Moreover, the a.s. convergence rates of the supremum of $|f_{n,K}(x)-Ef_{n,K}(x)|$ over a compact set and th","authors_text":"Yuexu Zhao, Zhengyan Lin","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-05-25T03:03:02Z","title":"Limit theorems for kernel density estimators under dependent samples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5882","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":"sha256:54961dfaaf23d19eb294000f4b8414f713659952966ede51569bad4f00b5bcf4","target":"record","created_at":"2026-05-18T03:21:42Z","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":"4efb286c69fe65f5b056e38a4820999d2116ee900642d65b960a337c5ce32b7f","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-05-25T03:03:02Z","title_canon_sha256":"29e62083926facf00aa0a49b26afd4f284f56c5d2e4c28e73e8bec9e1026bcb8"},"schema_version":"1.0","source":{"id":"1305.5882","kind":"arxiv","version":2}},"canonical_sha256":"1151ffc5ceec0ce9b9971eee906a9db8495091355e40a5e8b01436dac2204197","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1151ffc5ceec0ce9b9971eee906a9db8495091355e40a5e8b01436dac2204197","first_computed_at":"2026-05-18T03:21:42.987911Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:42.987911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u0QGSQjtQqo4liavNbulPjw7qQ7jviGKlAGr/lX9+X2DrstMJEIh0R2F8A2sgU81WPDcdsg1KfqnqWP4S7fxAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:42.988480Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.5882","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54961dfaaf23d19eb294000f4b8414f713659952966ede51569bad4f00b5bcf4","sha256:9eaee738d764be053a2cbe41196fc7df6476bbac038151cdc1261a7200a037ee"],"state_sha256":"bc3461e3b29525bdd6115047d8b812d074551d4518f77bfd0aff4d437c13cddd"}