{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JA5MYPRAYOZKCKH4DUEQ3SGRZM","short_pith_number":"pith:JA5MYPRA","canonical_record":{"source":{"id":"1210.5165","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-10-18T16:04:06Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"1aeaeab3404c216e1c9e551a2667390c475a05d91a8f7c36b9be14869e938f05","abstract_canon_sha256":"7f6638c98fc7321b96aa71c2ab1fc16a572cbb71aeab68ec2786b4686821542b"},"schema_version":"1.0"},"canonical_sha256":"483acc3e20c3b2a128fc1d090dc8d1cb31bb25476b3f3624b9f3dcf07e6f328e","source":{"kind":"arxiv","id":"1210.5165","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5165","created_at":"2026-05-18T03:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5165v1","created_at":"2026-05-18T03:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5165","created_at":"2026-05-18T03:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"JA5MYPRAYOZK","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JA5MYPRAYOZKCKH4","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JA5MYPRA","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JA5MYPRAYOZKCKH4DUEQ3SGRZM","target":"record","payload":{"canonical_record":{"source":{"id":"1210.5165","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-10-18T16:04:06Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"1aeaeab3404c216e1c9e551a2667390c475a05d91a8f7c36b9be14869e938f05","abstract_canon_sha256":"7f6638c98fc7321b96aa71c2ab1fc16a572cbb71aeab68ec2786b4686821542b"},"schema_version":"1.0"},"canonical_sha256":"483acc3e20c3b2a128fc1d090dc8d1cb31bb25476b3f3624b9f3dcf07e6f328e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:53.716175Z","signature_b64":"g2GnvG/cZdfM+liENqhR6/UVDSWhTaySQ/0oCP5bWuEkHhNDeb0W68gOkGMomcmyjcTEAEHvzPJxYIz8mv5AAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"483acc3e20c3b2a128fc1d090dc8d1cb31bb25476b3f3624b9f3dcf07e6f328e","last_reissued_at":"2026-05-18T03:42:53.715732Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:53.715732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.5165","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":"2026-05-18T03:42:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1AsuQkswDGHSaCWnzcN+SfyZRrwBcCDKVVhWrx/tnSZ8DOb3H7veqZXDvq9+zqhBtw8WpJqlKTnmkN9orwddAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:57:28.469821Z"},"content_sha256":"8def348b17fc7068968468db6c4d5742f7e1abab52c0f6c33d4399b5ce083fcd","schema_version":"1.0","event_id":"sha256:8def348b17fc7068968468db6c4d5742f7e1abab52c0f6c33d4399b5ce083fcd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JA5MYPRAYOZKCKH4DUEQ3SGRZM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimation of the transition density of a Markov chain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Mathieu Sart","submitted_at":"2012-10-18T16:04:06Z","abstract_excerpt":"We present two data-driven procedures to estimate the transition density of an homogeneous Markov chain. The first yields to a piecewise constant estimator on a suitable random partition. By using an Hellinger-type loss, we establish non-asymptotic risk bounds for our estimator when the square root of the transition density belongs to possibly inhomogeneous Besov spaces with possibly small regularity index. Some simulations are also provided. The second procedure is of theoretical interest and leads to a general model selection theorem from which we derive rates of convergence over a very wide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5165","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":"2026-05-18T03:42:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Up7m7c6DJOOlgHMrlgovsMrgxD0MxGItukXKw/jJBMrKYOWb58iwzJQ9qjHBxL0fVuwOwmdp0gu9S5sMnVbuBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:57:28.470153Z"},"content_sha256":"22c258abc14bb17ab2da0bef73382fb5589176ef7d3acd6afe7beef573f44bad","schema_version":"1.0","event_id":"sha256:22c258abc14bb17ab2da0bef73382fb5589176ef7d3acd6afe7beef573f44bad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JA5MYPRAYOZKCKH4DUEQ3SGRZM/bundle.json","state_url":"https://pith.science/pith/JA5MYPRAYOZKCKH4DUEQ3SGRZM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JA5MYPRAYOZKCKH4DUEQ3SGRZM/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":"2026-06-09T09:57:28Z","links":{"resolver":"https://pith.science/pith/JA5MYPRAYOZKCKH4DUEQ3SGRZM","bundle":"https://pith.science/pith/JA5MYPRAYOZKCKH4DUEQ3SGRZM/bundle.json","state":"https://pith.science/pith/JA5MYPRAYOZKCKH4DUEQ3SGRZM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JA5MYPRAYOZKCKH4DUEQ3SGRZM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JA5MYPRAYOZKCKH4DUEQ3SGRZM","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":"7f6638c98fc7321b96aa71c2ab1fc16a572cbb71aeab68ec2786b4686821542b","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-10-18T16:04:06Z","title_canon_sha256":"1aeaeab3404c216e1c9e551a2667390c475a05d91a8f7c36b9be14869e938f05"},"schema_version":"1.0","source":{"id":"1210.5165","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5165","created_at":"2026-05-18T03:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5165v1","created_at":"2026-05-18T03:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5165","created_at":"2026-05-18T03:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"JA5MYPRAYOZK","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JA5MYPRAYOZKCKH4","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JA5MYPRA","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:22c258abc14bb17ab2da0bef73382fb5589176ef7d3acd6afe7beef573f44bad","target":"graph","created_at":"2026-05-18T03:42:53Z","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 present two data-driven procedures to estimate the transition density of an homogeneous Markov chain. The first yields to a piecewise constant estimator on a suitable random partition. By using an Hellinger-type loss, we establish non-asymptotic risk bounds for our estimator when the square root of the transition density belongs to possibly inhomogeneous Besov spaces with possibly small regularity index. Some simulations are also provided. The second procedure is of theoretical interest and leads to a general model selection theorem from which we derive rates of convergence over a very wide","authors_text":"Mathieu Sart","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-10-18T16:04:06Z","title":"Estimation of the transition density of a Markov chain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5165","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":"sha256:8def348b17fc7068968468db6c4d5742f7e1abab52c0f6c33d4399b5ce083fcd","target":"record","created_at":"2026-05-18T03:42:53Z","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":"7f6638c98fc7321b96aa71c2ab1fc16a572cbb71aeab68ec2786b4686821542b","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-10-18T16:04:06Z","title_canon_sha256":"1aeaeab3404c216e1c9e551a2667390c475a05d91a8f7c36b9be14869e938f05"},"schema_version":"1.0","source":{"id":"1210.5165","kind":"arxiv","version":1}},"canonical_sha256":"483acc3e20c3b2a128fc1d090dc8d1cb31bb25476b3f3624b9f3dcf07e6f328e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"483acc3e20c3b2a128fc1d090dc8d1cb31bb25476b3f3624b9f3dcf07e6f328e","first_computed_at":"2026-05-18T03:42:53.715732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:53.715732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g2GnvG/cZdfM+liENqhR6/UVDSWhTaySQ/0oCP5bWuEkHhNDeb0W68gOkGMomcmyjcTEAEHvzPJxYIz8mv5AAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:53.716175Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.5165","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8def348b17fc7068968468db6c4d5742f7e1abab52c0f6c33d4399b5ce083fcd","sha256:22c258abc14bb17ab2da0bef73382fb5589176ef7d3acd6afe7beef573f44bad"],"state_sha256":"982cbb22e7e951b915b4bf878730b5bc2963fe56e0d6af6497ce2f2fe18af621"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L0Y0huGOhv9+PNWgroKrMmLGSjFLlK6RHMBhsjQgN1B3C+NhUbv7/atUK+KycEuQnHGUxJExgCkiVtTN/0oXBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T09:57:28.471951Z","bundle_sha256":"29f17e1d128fc29a5a22baef37a16de46a0b55c9764e958d7e8417345530a168"}}