{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:UWJM6GJKHVI6CMF45IWEJ2QDXT","short_pith_number":"pith:UWJM6GJK","schema_version":"1.0","canonical_sha256":"a592cf192a3d51e130bcea2c44ea03bcc2cf397894f94397b5b029b1709aa82d","source":{"kind":"arxiv","id":"1104.4396","version":1},"attestation_state":"computed","paper":{"title":"Limit theorems for functions of marginal quantiles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"G. Jogesh Babu, Kwok Pui Choi, Vasudevan Mangalam, Zhidong Bai","submitted_at":"2011-04-22T06:47:28Z","abstract_excerpt":"Multivariate distributions are explored using the joint distributions of marginal sample quantiles. Limit theory for the mean of a function of order statistics is presented. The results include a multivariate central limit theorem and a strong law of large numbers. A result similar to Bahadur's representation of quantiles is established for the mean of a function of the marginal quantiles. In particular, it is shown that \\[\\sqrt{n}\\Biggl(\\frac{1}{n}\\sum_{i=1}^n\\phi\\bigl(X_{n:i}^{(1)},...,X_{n:i}^{(d)}\\bigr)-\\bar{\\gamma}\\Biggr)=\\frac{1}{\\sqrt{n}}\\sum_{i=1}^nZ_{n,i}+\\mathrm{o}_P(1)\\] as $n\\right"},"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":"1104.4396","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-04-22T06:47:28Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"92f00e3d4f4a9dfae9294981c0670c52407780ba4319301cda0db81a23849dc7","abstract_canon_sha256":"3ec08f71cc4dadfb4c84ca5d96b3da6d01a86409a71b75a14974444c72a9239e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:34.717249Z","signature_b64":"XjHVktHWe+AtPgwfijviKKz6xNsbuBRUsq9e6+VaSuBTd1Xie4iDUhJDwFJ3nPOhfartbspgGNQBnD2gfoXEDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a592cf192a3d51e130bcea2c44ea03bcc2cf397894f94397b5b029b1709aa82d","last_reissued_at":"2026-05-18T04:23:34.716691Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:34.716691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Limit theorems for functions of marginal quantiles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"G. Jogesh Babu, Kwok Pui Choi, Vasudevan Mangalam, Zhidong Bai","submitted_at":"2011-04-22T06:47:28Z","abstract_excerpt":"Multivariate distributions are explored using the joint distributions of marginal sample quantiles. Limit theory for the mean of a function of order statistics is presented. The results include a multivariate central limit theorem and a strong law of large numbers. A result similar to Bahadur's representation of quantiles is established for the mean of a function of the marginal quantiles. In particular, it is shown that \\[\\sqrt{n}\\Biggl(\\frac{1}{n}\\sum_{i=1}^n\\phi\\bigl(X_{n:i}^{(1)},...,X_{n:i}^{(d)}\\bigr)-\\bar{\\gamma}\\Biggr)=\\frac{1}{\\sqrt{n}}\\sum_{i=1}^nZ_{n,i}+\\mathrm{o}_P(1)\\] as $n\\right"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4396","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":"1104.4396","created_at":"2026-05-18T04:23:34.716782+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.4396v1","created_at":"2026-05-18T04:23:34.716782+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4396","created_at":"2026-05-18T04:23:34.716782+00:00"},{"alias_kind":"pith_short_12","alias_value":"UWJM6GJKHVI6","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"UWJM6GJKHVI6CMF4","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"UWJM6GJK","created_at":"2026-05-18T12:26:42.757692+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/UWJM6GJKHVI6CMF45IWEJ2QDXT","json":"https://pith.science/pith/UWJM6GJKHVI6CMF45IWEJ2QDXT.json","graph_json":"https://pith.science/api/pith-number/UWJM6GJKHVI6CMF45IWEJ2QDXT/graph.json","events_json":"https://pith.science/api/pith-number/UWJM6GJKHVI6CMF45IWEJ2QDXT/events.json","paper":"https://pith.science/paper/UWJM6GJK"},"agent_actions":{"view_html":"https://pith.science/pith/UWJM6GJKHVI6CMF45IWEJ2QDXT","download_json":"https://pith.science/pith/UWJM6GJKHVI6CMF45IWEJ2QDXT.json","view_paper":"https://pith.science/paper/UWJM6GJK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.4396&json=true","fetch_graph":"https://pith.science/api/pith-number/UWJM6GJKHVI6CMF45IWEJ2QDXT/graph.json","fetch_events":"https://pith.science/api/pith-number/UWJM6GJKHVI6CMF45IWEJ2QDXT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UWJM6GJKHVI6CMF45IWEJ2QDXT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UWJM6GJKHVI6CMF45IWEJ2QDXT/action/storage_attestation","attest_author":"https://pith.science/pith/UWJM6GJKHVI6CMF45IWEJ2QDXT/action/author_attestation","sign_citation":"https://pith.science/pith/UWJM6GJKHVI6CMF45IWEJ2QDXT/action/citation_signature","submit_replication":"https://pith.science/pith/UWJM6GJKHVI6CMF45IWEJ2QDXT/action/replication_record"}},"created_at":"2026-05-18T04:23:34.716782+00:00","updated_at":"2026-05-18T04:23:34.716782+00:00"}