{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:QVDT7S4EGAGUTQGE3WT5GPA364","short_pith_number":"pith:QVDT7S4E","schema_version":"1.0","canonical_sha256":"85473fcb84300d49c0c4dda7d33c1bf73b1689c7d31c24e26e9fdb8d1450d515","source":{"kind":"arxiv","id":"1111.4591","version":1},"attestation_state":"computed","paper":{"title":"Empirical Quantile CLTs for Time Dependent Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"James Kuelbs, Joel Zinn","submitted_at":"2011-11-19T22:29:05Z","abstract_excerpt":"We establish empirical quantile process CLTs based on $n$ independent copies of a stochastic process $\\{X_t: t \\in E\\}$ that are uniform in $t \\in E$ and quantile levels $\\alpha \\in I$, where $I$ is a closed sub-interval of $(0,1)$. Typically $E=[0,T]$, or a finite product of such intervals. Also included are CLT's for the empirical process based on $\\{I_{X_t \\le y} - \\rm {Pr}(X_t \\le y): t \\in E, y \\in R \\}$ that are uniform in $t \\in E, y \\in R$. The process $\\{X_t: t \\in E\\}$ may be chosen from a broad collection of Gaussian processes, compound Poisson processes, stationary independent incr"},"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":"1111.4591","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-19T22:29:05Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"bbe92fec77a5140d5f710ff4d098f546186ab60af5e761342ecf17524b847320","abstract_canon_sha256":"9a7b26a5d81748b72b7593a9d2e6870bac8711ac71621aacfe80496f231c8d4e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:03.031349Z","signature_b64":"6f9bi1Ktfwxb6rA9v3RkC38Dr3/BjSQF0Di3iwSM0ewidYdr7VWXAnDWcgLmdlr8aFgEWX/Ou0+9L38q60lZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85473fcb84300d49c0c4dda7d33c1bf73b1689c7d31c24e26e9fdb8d1450d515","last_reissued_at":"2026-05-18T04:08:03.030893Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:03.030893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Empirical Quantile CLTs for Time Dependent Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"James Kuelbs, Joel Zinn","submitted_at":"2011-11-19T22:29:05Z","abstract_excerpt":"We establish empirical quantile process CLTs based on $n$ independent copies of a stochastic process $\\{X_t: t \\in E\\}$ that are uniform in $t \\in E$ and quantile levels $\\alpha \\in I$, where $I$ is a closed sub-interval of $(0,1)$. Typically $E=[0,T]$, or a finite product of such intervals. Also included are CLT's for the empirical process based on $\\{I_{X_t \\le y} - \\rm {Pr}(X_t \\le y): t \\in E, y \\in R \\}$ that are uniform in $t \\in E, y \\in R$. The process $\\{X_t: t \\in E\\}$ may be chosen from a broad collection of Gaussian processes, compound Poisson processes, stationary independent incr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4591","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1111.4591","created_at":"2026-05-18T04:08:03.030953+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.4591v1","created_at":"2026-05-18T04:08:03.030953+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4591","created_at":"2026-05-18T04:08:03.030953+00:00"},{"alias_kind":"pith_short_12","alias_value":"QVDT7S4EGAGU","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"QVDT7S4EGAGUTQGE","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"QVDT7S4E","created_at":"2026-05-18T12:26:39.201973+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QVDT7S4EGAGUTQGE3WT5GPA364","json":"https://pith.science/pith/QVDT7S4EGAGUTQGE3WT5GPA364.json","graph_json":"https://pith.science/api/pith-number/QVDT7S4EGAGUTQGE3WT5GPA364/graph.json","events_json":"https://pith.science/api/pith-number/QVDT7S4EGAGUTQGE3WT5GPA364/events.json","paper":"https://pith.science/paper/QVDT7S4E"},"agent_actions":{"view_html":"https://pith.science/pith/QVDT7S4EGAGUTQGE3WT5GPA364","download_json":"https://pith.science/pith/QVDT7S4EGAGUTQGE3WT5GPA364.json","view_paper":"https://pith.science/paper/QVDT7S4E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.4591&json=true","fetch_graph":"https://pith.science/api/pith-number/QVDT7S4EGAGUTQGE3WT5GPA364/graph.json","fetch_events":"https://pith.science/api/pith-number/QVDT7S4EGAGUTQGE3WT5GPA364/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QVDT7S4EGAGUTQGE3WT5GPA364/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QVDT7S4EGAGUTQGE3WT5GPA364/action/storage_attestation","attest_author":"https://pith.science/pith/QVDT7S4EGAGUTQGE3WT5GPA364/action/author_attestation","sign_citation":"https://pith.science/pith/QVDT7S4EGAGUTQGE3WT5GPA364/action/citation_signature","submit_replication":"https://pith.science/pith/QVDT7S4EGAGUTQGE3WT5GPA364/action/replication_record"}},"created_at":"2026-05-18T04:08:03.030953+00:00","updated_at":"2026-05-18T04:08:03.030953+00:00"}