{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TQD7SJ4H6FLAKVLM23CSWNA2B3","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":"f8438e0725e1d247df949ca90bd7262ea21a6591e60dfeb0814c2edef00db0c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-02-28T16:00:20Z","title_canon_sha256":"5b1668eff3e41bc34485a89223088264cb8a3beda00f3eb77da175690df6026b"},"schema_version":"1.0","source":{"id":"1202.6263","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6263","created_at":"2026-05-18T04:01:13Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6263v1","created_at":"2026-05-18T04:01:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6263","created_at":"2026-05-18T04:01:13Z"},{"alias_kind":"pith_short_12","alias_value":"TQD7SJ4H6FLA","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TQD7SJ4H6FLAKVLM","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TQD7SJ4H","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:5f74d7b2caf84c2892b2260bd39d9233e67e3a894dbd7d1c98acc44bc434887a","target":"graph","created_at":"2026-05-18T04:01:13Z","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":"Non-parametric estimation of a convex discrete distribution may be of interest in several applications, such as the estimation of species abundance distribution in ecology. In this paper we study the least squares estimator of a discrete distribution under the constraint of convexity. We show that this estimator exists and is unique, and that it always outperforms the classical empirical estimator in terms of the $\\ell_{2}$-distance. We provide an algorithm for its computation, based on the support reduction algorithm. We compare its performance to those of the empirical estimator, on the basi","authors_text":"C\\'ecile Durot, Fran\\c{c}ois Koladjo, St\\'ephane Robin, Sylvie Huet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-02-28T16:00:20Z","title":"Estimation of a convex discrete distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6263","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":"sha256:308ed58cb58e4b9d3543b6177c6f0f0507b869cbeb4bb620f6350f9fc524fca4","target":"record","created_at":"2026-05-18T04:01:13Z","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":"f8438e0725e1d247df949ca90bd7262ea21a6591e60dfeb0814c2edef00db0c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-02-28T16:00:20Z","title_canon_sha256":"5b1668eff3e41bc34485a89223088264cb8a3beda00f3eb77da175690df6026b"},"schema_version":"1.0","source":{"id":"1202.6263","kind":"arxiv","version":1}},"canonical_sha256":"9c07f92787f15605556cd6c52b341a0ed606ca64cd73dee72d6a08f7aa7f59b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c07f92787f15605556cd6c52b341a0ed606ca64cd73dee72d6a08f7aa7f59b6","first_computed_at":"2026-05-18T04:01:13.841563Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:13.841563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oRq1SymABxVnDKzhIp6UGHueE6zed+xf9mg2GMCyh0iToWz/lTeMziMsIAbfkrghwDTpayTqMO4E3Y0EkARnCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:13.842263Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.6263","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:308ed58cb58e4b9d3543b6177c6f0f0507b869cbeb4bb620f6350f9fc524fca4","sha256:5f74d7b2caf84c2892b2260bd39d9233e67e3a894dbd7d1c98acc44bc434887a"],"state_sha256":"856a3f3e76a702242d70d0ce52b739991641e64a759527ed102338385563ef98"}