{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:LBNBYK5A7WR5ZNAHHSAAH5L4ZQ","short_pith_number":"pith:LBNBYK5A","schema_version":"1.0","canonical_sha256":"585a1c2ba0fda3dcb4073c8003f57ccc2c01227ebdbd20bc8b0b322eb2a6eba4","source":{"kind":"arxiv","id":"2603.27843","version":2},"attestation_state":"computed","paper":{"title":"Empirical Bayes Estimation and Inference via Smooth Nonparametric Maximum Likelihood","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Bodhisattva Sen, Taehyun Kim","submitted_at":"2026-03-29T19:59:00Z","abstract_excerpt":"The empirical Bayes $g$-modeling approach based on the nonparametric maximum likelihood estimator (NPMLE) has been central to large-scale estimation and inference in the normal means problem. However, theoretical guarantees for uncertainty quantification remain scarce. A key obstacle is that the NPMLE is necessarily discrete, which yields discrete posterior credible sets and a slow logarithmic deconvolution rate. We address both limitations by introducing a hierarchical Gaussian smoothing layer that restricts the mixing distribution to a Gaussian location mixture. Our smooth NPMLE inherits the"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2603.27843","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-03-29T19:59:00Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"f30b70e24df838ee35f5926804f9ccc7194d26fe7496bb2f99f324b22b9a6b8b","abstract_canon_sha256":"53b72a1bae7e282905ec4a14d846560c056666e7905337993cc67add02bf2780"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-11T01:09:33.936421Z","signature_b64":"JpkIWJR8zCthyScTqKs0c9Km27ET7cCp2y/i+X0NCBJPYuNyUvQWJp80BjkkIcwM7qwqPfQv7fN//jeV4x3PBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"585a1c2ba0fda3dcb4073c8003f57ccc2c01227ebdbd20bc8b0b322eb2a6eba4","last_reissued_at":"2026-06-11T01:09:33.935465Z","signature_status":"signed_v1","first_computed_at":"2026-06-11T01:09:33.935465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Empirical Bayes Estimation and Inference via Smooth Nonparametric Maximum Likelihood","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Bodhisattva Sen, Taehyun Kim","submitted_at":"2026-03-29T19:59:00Z","abstract_excerpt":"The empirical Bayes $g$-modeling approach based on the nonparametric maximum likelihood estimator (NPMLE) has been central to large-scale estimation and inference in the normal means problem. However, theoretical guarantees for uncertainty quantification remain scarce. A key obstacle is that the NPMLE is necessarily discrete, which yields discrete posterior credible sets and a slow logarithmic deconvolution rate. We address both limitations by introducing a hierarchical Gaussian smoothing layer that restricts the mixing distribution to a Gaussian location mixture. Our smooth NPMLE inherits the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.27843","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.27843/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2603.27843","created_at":"2026-06-11T01:09:33.935572+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.27843v2","created_at":"2026-06-11T01:09:33.935572+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.27843","created_at":"2026-06-11T01:09:33.935572+00:00"},{"alias_kind":"pith_short_12","alias_value":"LBNBYK5A7WR5","created_at":"2026-06-11T01:09:33.935572+00:00"},{"alias_kind":"pith_short_16","alias_value":"LBNBYK5A7WR5ZNAH","created_at":"2026-06-11T01:09:33.935572+00:00"},{"alias_kind":"pith_short_8","alias_value":"LBNBYK5A","created_at":"2026-06-11T01:09:33.935572+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2605.03594","citing_title":"Poisson Empirical Bayes via Gamma-Smoothed Nonparametric Maximum Likelihood","ref_index":30,"is_internal_anchor":true},{"citing_arxiv_id":"2605.02070","citing_title":"Sharp regret-Hellinger bounds for Gaussian empirical Bayes via polynomial approximation","ref_index":26,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LBNBYK5A7WR5ZNAHHSAAH5L4ZQ","json":"https://pith.science/pith/LBNBYK5A7WR5ZNAHHSAAH5L4ZQ.json","graph_json":"https://pith.science/api/pith-number/LBNBYK5A7WR5ZNAHHSAAH5L4ZQ/graph.json","events_json":"https://pith.science/api/pith-number/LBNBYK5A7WR5ZNAHHSAAH5L4ZQ/events.json","paper":"https://pith.science/paper/LBNBYK5A"},"agent_actions":{"view_html":"https://pith.science/pith/LBNBYK5A7WR5ZNAHHSAAH5L4ZQ","download_json":"https://pith.science/pith/LBNBYK5A7WR5ZNAHHSAAH5L4ZQ.json","view_paper":"https://pith.science/paper/LBNBYK5A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.27843&json=true","fetch_graph":"https://pith.science/api/pith-number/LBNBYK5A7WR5ZNAHHSAAH5L4ZQ/graph.json","fetch_events":"https://pith.science/api/pith-number/LBNBYK5A7WR5ZNAHHSAAH5L4ZQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LBNBYK5A7WR5ZNAHHSAAH5L4ZQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LBNBYK5A7WR5ZNAHHSAAH5L4ZQ/action/storage_attestation","attest_author":"https://pith.science/pith/LBNBYK5A7WR5ZNAHHSAAH5L4ZQ/action/author_attestation","sign_citation":"https://pith.science/pith/LBNBYK5A7WR5ZNAHHSAAH5L4ZQ/action/citation_signature","submit_replication":"https://pith.science/pith/LBNBYK5A7WR5ZNAHHSAAH5L4ZQ/action/replication_record"}},"created_at":"2026-06-11T01:09:33.935572+00:00","updated_at":"2026-06-11T01:09:33.935572+00:00"}