{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:442P7W6CV6CWXD37V3AQ7QIMKN","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":"db605f09d174d698971c32cc30c382e4af8de6a75851954878112d36cf94f82d","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-02-12T22:14:42Z","title_canon_sha256":"ef8d2d4ebca5e09c134e7629e6bbb4988e494ace057488ea16849ebbbe872902"},"schema_version":"1.0","source":{"id":"1402.2997","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2997","created_at":"2026-05-18T02:31:30Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2997v3","created_at":"2026-05-18T02:31:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2997","created_at":"2026-05-18T02:31:30Z"},{"alias_kind":"pith_short_12","alias_value":"442P7W6CV6CW","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"442P7W6CV6CWXD37","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"442P7W6C","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:a2d01c0babb1cf2bf354e106a611d8aad81887ee1062e33a59def191571315e1","target":"graph","created_at":"2026-05-18T02:31:30Z","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 give a general result on the effective degrees of freedom for nonlinear least squares estimation, which relates the degrees of freedom to the divergence of the estimator. We show that in a general framework, the divergence of the least squares estimator is a well defined but potentially negatively biased estimate of the degrees of freedom, and we give an exact representation of the bias. This implies that if we use the divergence as a plug-in estimate of the degrees of freedom in Stein's unbiased risk estimate (SURE), we generally underestimate the true risk. Our result applies, for instanc","authors_text":"Alexander Sokol, Niels Richard Hansen","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-02-12T22:14:42Z","title":"Degrees of freedom for nonlinear least squares estimation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2997","kind":"arxiv","version":3},"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":"sha256:1e73022ae9abedc8a00cd8ab7f73b98754a52d8839e0a4b6a08efee8d0e50ebe","target":"record","created_at":"2026-05-18T02:31:30Z","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":"db605f09d174d698971c32cc30c382e4af8de6a75851954878112d36cf94f82d","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-02-12T22:14:42Z","title_canon_sha256":"ef8d2d4ebca5e09c134e7629e6bbb4988e494ace057488ea16849ebbbe872902"},"schema_version":"1.0","source":{"id":"1402.2997","kind":"arxiv","version":3}},"canonical_sha256":"e734ffdbc2af856b8f7faec10fc10c536734009f91e9debabc3fed20c1b64db7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e734ffdbc2af856b8f7faec10fc10c536734009f91e9debabc3fed20c1b64db7","first_computed_at":"2026-05-18T02:31:30.085498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:30.085498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tF1rLAEp9nK+SE3NGfeGH0yYdm95prXGA2GuyGyccXXARl1229SwhCKQaJJZDULhKqpRqlw00FBldGVAEHLWAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:30.085911Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.2997","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e73022ae9abedc8a00cd8ab7f73b98754a52d8839e0a4b6a08efee8d0e50ebe","sha256:a2d01c0babb1cf2bf354e106a611d8aad81887ee1062e33a59def191571315e1"],"state_sha256":"ef1aaad96101684f86acc70d2b3da5d8b08e0f869a661646200bcfbd4986571b"}