{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:4NDBVJJAQ74A67OHJXXSYVUA3Q","short_pith_number":"pith:4NDBVJJA","canonical_record":{"source":{"id":"1408.5297","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-08-22T14:06:58Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"82403bf4d4421e50ec2ad7fd1676da628c9e8bac5925a6917f3217ad8e26396f","abstract_canon_sha256":"98401acdf470f265acba4d0654d29bec72265fa2f5371d8ebbba54229fdae476"},"schema_version":"1.0"},"canonical_sha256":"e3461aa52087f80f7dc74def2c5680dc1028bc7dab4d00708a0665dabc215297","source":{"kind":"arxiv","id":"1408.5297","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5297","created_at":"2026-05-18T02:44:33Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5297v1","created_at":"2026-05-18T02:44:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5297","created_at":"2026-05-18T02:44:33Z"},{"alias_kind":"pith_short_12","alias_value":"4NDBVJJAQ74A","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4NDBVJJAQ74A67OH","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4NDBVJJA","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:4NDBVJJAQ74A67OHJXXSYVUA3Q","target":"record","payload":{"canonical_record":{"source":{"id":"1408.5297","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-08-22T14:06:58Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"82403bf4d4421e50ec2ad7fd1676da628c9e8bac5925a6917f3217ad8e26396f","abstract_canon_sha256":"98401acdf470f265acba4d0654d29bec72265fa2f5371d8ebbba54229fdae476"},"schema_version":"1.0"},"canonical_sha256":"e3461aa52087f80f7dc74def2c5680dc1028bc7dab4d00708a0665dabc215297","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:33.427618Z","signature_b64":"Oowtp5PKV5nnNocnQ3auEP0psQhZO4RA14QVJZRYt7sg85a7EUckXbRyeyTLxvx4F7UV3N2ccOEO03ShhQ2bDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3461aa52087f80f7dc74def2c5680dc1028bc7dab4d00708a0665dabc215297","last_reissued_at":"2026-05-18T02:44:33.427029Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:33.427029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.5297","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7PeCLlZDyN/orIuyztcaquVMOzCGcUI10k4vsTb0Mey35r/aCrmUjjaalfSjswB5LwTep0fmpwVcAIjHp9mTCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T17:17:33.991148Z"},"content_sha256":"c434ad22846f547352ab0db223bd3c4c01af786c934213b512bb3bfca6388656","schema_version":"1.0","event_id":"sha256:c434ad22846f547352ab0db223bd3c4c01af786c934213b512bb3bfca6388656"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:4NDBVJJAQ74A67OHJXXSYVUA3Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Predictive Density Estimation for Location Families under Integrated $L_2$ and $L_1$ Losses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"\\'Eric Marchand, Tatsuya Kubokawa, William E. Strawderman","submitted_at":"2014-08-22T14:06:58Z","abstract_excerpt":"Our investigation concerns the estimation of predictive densities and a study of efficiency as measured by the frequentist risk of such predictive densities with integrated $L_2$ and $L_1$ losses. Our findings relate to a $p-$variate spherically symmetric observable $X \\sim p_X(\\|x-\\mu\\|^2)$ and the objective of estimating the density of $Y \\sim q_Y(\\|y-\\mu\\|^2)$ based on $X$. For $L_2$ loss, we describe Bayes estimation, minimum risk equivariant estimation (MRE), and minimax estimation. We focus on the risk performance of the benchmark minimum risk equivariant estimator, plug-in estimators, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5297","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EMkDd8+jLgmvbKOV3+lTLrce3VF/r9SnZDZN+VBxhzqJ4HteKIbDcT9B7OfPiaKsPxny+A/SLjwo5x4A/hg6Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T17:17:33.991507Z"},"content_sha256":"7e9255f9cdd8d8944978a122001da9de551b4d4de5be0b3b7d8cb5ae4bcdd65c","schema_version":"1.0","event_id":"sha256:7e9255f9cdd8d8944978a122001da9de551b4d4de5be0b3b7d8cb5ae4bcdd65c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4NDBVJJAQ74A67OHJXXSYVUA3Q/bundle.json","state_url":"https://pith.science/pith/4NDBVJJAQ74A67OHJXXSYVUA3Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4NDBVJJAQ74A67OHJXXSYVUA3Q/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-30T17:17:33Z","links":{"resolver":"https://pith.science/pith/4NDBVJJAQ74A67OHJXXSYVUA3Q","bundle":"https://pith.science/pith/4NDBVJJAQ74A67OHJXXSYVUA3Q/bundle.json","state":"https://pith.science/pith/4NDBVJJAQ74A67OHJXXSYVUA3Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4NDBVJJAQ74A67OHJXXSYVUA3Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4NDBVJJAQ74A67OHJXXSYVUA3Q","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":"98401acdf470f265acba4d0654d29bec72265fa2f5371d8ebbba54229fdae476","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-08-22T14:06:58Z","title_canon_sha256":"82403bf4d4421e50ec2ad7fd1676da628c9e8bac5925a6917f3217ad8e26396f"},"schema_version":"1.0","source":{"id":"1408.5297","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5297","created_at":"2026-05-18T02:44:33Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5297v1","created_at":"2026-05-18T02:44:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5297","created_at":"2026-05-18T02:44:33Z"},{"alias_kind":"pith_short_12","alias_value":"4NDBVJJAQ74A","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4NDBVJJAQ74A67OH","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4NDBVJJA","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:7e9255f9cdd8d8944978a122001da9de551b4d4de5be0b3b7d8cb5ae4bcdd65c","target":"graph","created_at":"2026-05-18T02:44:33Z","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":"Our investigation concerns the estimation of predictive densities and a study of efficiency as measured by the frequentist risk of such predictive densities with integrated $L_2$ and $L_1$ losses. Our findings relate to a $p-$variate spherically symmetric observable $X \\sim p_X(\\|x-\\mu\\|^2)$ and the objective of estimating the density of $Y \\sim q_Y(\\|y-\\mu\\|^2)$ based on $X$. For $L_2$ loss, we describe Bayes estimation, minimum risk equivariant estimation (MRE), and minimax estimation. We focus on the risk performance of the benchmark minimum risk equivariant estimator, plug-in estimators, a","authors_text":"\\'Eric Marchand, Tatsuya Kubokawa, William E. Strawderman","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-08-22T14:06:58Z","title":"On Predictive Density Estimation for Location Families under Integrated $L_2$ and $L_1$ Losses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5297","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:c434ad22846f547352ab0db223bd3c4c01af786c934213b512bb3bfca6388656","target":"record","created_at":"2026-05-18T02:44:33Z","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":"98401acdf470f265acba4d0654d29bec72265fa2f5371d8ebbba54229fdae476","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-08-22T14:06:58Z","title_canon_sha256":"82403bf4d4421e50ec2ad7fd1676da628c9e8bac5925a6917f3217ad8e26396f"},"schema_version":"1.0","source":{"id":"1408.5297","kind":"arxiv","version":1}},"canonical_sha256":"e3461aa52087f80f7dc74def2c5680dc1028bc7dab4d00708a0665dabc215297","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3461aa52087f80f7dc74def2c5680dc1028bc7dab4d00708a0665dabc215297","first_computed_at":"2026-05-18T02:44:33.427029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:33.427029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Oowtp5PKV5nnNocnQ3auEP0psQhZO4RA14QVJZRYt7sg85a7EUckXbRyeyTLxvx4F7UV3N2ccOEO03ShhQ2bDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:33.427618Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5297","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c434ad22846f547352ab0db223bd3c4c01af786c934213b512bb3bfca6388656","sha256:7e9255f9cdd8d8944978a122001da9de551b4d4de5be0b3b7d8cb5ae4bcdd65c"],"state_sha256":"897a597eea5d5a2fe9589a308c57a8bcfe36529a5b9b332c15ae3a7bb0447c5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yhuo+iD5Vskp5J4WsCoDynsdcvmsMy+RsRYaimHI1m0aSkNyq3nr/qYLKo6TfSaplrj2Go6HM2+dSYW/spdGAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T17:17:33.993408Z","bundle_sha256":"19d43a7a5e495a46923f6adc10eeaec097f1577430ee3f13be5d0edbcfc4d5a2"}}