{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:WC3SGX3SWUEGRWNQCYIKBN5664","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":"dd9fab27ad6b89eda4da9e4f42a86ab932ba039d59806150ad746168e0c91b53","cross_cats_sorted":["stat.TH"],"license":"","primary_cat":"math.ST","submitted_at":"2007-11-26T07:34:35Z","title_canon_sha256":"0fba03a0d2b969462767343383227b4bfc88a30e98be3ee7196e6b9fd165ffd5"},"schema_version":"1.0","source":{"id":"0711.3957","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.3957","created_at":"2026-05-18T04:09:04Z"},{"alias_kind":"arxiv_version","alias_value":"0711.3957v1","created_at":"2026-05-18T04:09:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.3957","created_at":"2026-05-18T04:09:04Z"},{"alias_kind":"pith_short_12","alias_value":"WC3SGX3SWUEG","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"WC3SGX3SWUEGRWNQ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"WC3SGX3S","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:7263f9985ee03d057f5fc2feae55a6a1dae57611e6b37f392f8e88b80b6724cf","target":"graph","created_at":"2026-05-18T04:09:04Z","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 investigate the moment estimation for an ergodic diffusion process with unknown trend coefficient. We consider nonparametric and parametric estimation. In each case, we present a lower bound for the risk and then construct an asymptotically efficient estimator of the moment type functional or of a parameter which has a one-to-one correspondence to such a functional. Next, we clarify a higher order property of the moment type estimator by the Edgeworth expansion of the distribution function.","authors_text":"nakahiro yoshida, Yury A. Kutoyants","cross_cats":["stat.TH"],"headline":"","license":"","primary_cat":"math.ST","submitted_at":"2007-11-26T07:34:35Z","title":"Moment estimation for ergodic diffusion processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.3957","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":"sha256:7f4fdd219931ec45eda1abad1a2864d646bacf9d7482f48e38a3d5315c438d73","target":"record","created_at":"2026-05-18T04:09:04Z","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":"dd9fab27ad6b89eda4da9e4f42a86ab932ba039d59806150ad746168e0c91b53","cross_cats_sorted":["stat.TH"],"license":"","primary_cat":"math.ST","submitted_at":"2007-11-26T07:34:35Z","title_canon_sha256":"0fba03a0d2b969462767343383227b4bfc88a30e98be3ee7196e6b9fd165ffd5"},"schema_version":"1.0","source":{"id":"0711.3957","kind":"arxiv","version":1}},"canonical_sha256":"b0b7235f72b50868d9b01610a0b7bef72c519cb4cbb3b875488a6ef8ff1b7825","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0b7235f72b50868d9b01610a0b7bef72c519cb4cbb3b875488a6ef8ff1b7825","first_computed_at":"2026-05-18T04:09:04.493134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:04.493134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UDzGuOtGa2nj2wuh0wMPDOa1iPH8PndPKTmPhc1UpugAXIY2pxh+OBI1DCMunitTMIMgKvfcqy7QN0nlOQzfBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:04.493648Z","signed_message":"canonical_sha256_bytes"},"source_id":"0711.3957","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f4fdd219931ec45eda1abad1a2864d646bacf9d7482f48e38a3d5315c438d73","sha256:7263f9985ee03d057f5fc2feae55a6a1dae57611e6b37f392f8e88b80b6724cf"],"state_sha256":"3d29c546d214663862ae38583f6705a9f7a8863d780edfdf1648be1521072a5e"}