{"paper":{"title":"Quantifying Dependence Between Random Vectors: A New Index with Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A new index for random vectors equals zero exactly when they are sub-independent and takes all values in [0,1].","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Chuancun Yin","submitted_at":"2026-05-16T12:43:35Z","abstract_excerpt":"This article proposes a new index for quantifying the degree of dependence between random vectors. The index takes values in [0,1] and equals zero if and only if the random vectors are sub-independent. Unlike mere uncorrelatedness, sub-independence implies a stronger form of dependence while remaining strictly weaker than full independence. The proposed index is constructed via characteristic functions and admits a simplified representation in terms of moments. We establish its theoretical properties and derive a computationally efficient formula for the corresponding empirical measure. Furthe"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The proposed index takes values in [0,1] and equals zero if and only if the random vectors are sub-independent.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the characteristic-function construction yields an index that is exactly zero under sub-independence and positive otherwise, as asserted without detailed derivation in the abstract.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Introduces a dependence index for random vectors in [0,1] that vanishes if and only if the vectors are sub-independent, constructed via characteristic functions with empirical and asymptotic results.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A new index for random vectors equals zero exactly when they are sub-independent and takes all values in [0,1].","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"74f6448bbb829e38a85e15f5d6f4c680ef93317a8a14d7abca6c261e0c74be68"},"source":{"id":"2605.16970","kind":"arxiv","version":1},"verdict":{"id":"d3f53492-437b-41a6-a833-699051f251df","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:44:42.275772Z","strongest_claim":"The proposed index takes values in [0,1] and equals zero if and only if the random vectors are sub-independent.","one_line_summary":"Introduces a dependence index for random vectors in [0,1] that vanishes if and only if the vectors are sub-independent, constructed via characteristic functions with empirical and asymptotic results.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the characteristic-function construction yields an index that is exactly zero under sub-independence and positive otherwise, as asserted without detailed derivation in the abstract.","pith_extraction_headline":"A new index for random vectors equals zero exactly when they are sub-independent and takes all values in [0,1]."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16970/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"cited_work_retraction","ran_at":"2026-05-19T19:51:57.215671Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"citation_quote_validity","ran_at":"2026-05-19T19:50:08.319567Z","status":"completed","version":"0.1.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T19:01:18.858817Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:51:21.771546Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T18:41:56.223418Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.309765Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"1a492a113d2a158c95383a32a6fbcff824505314be69c74336df8a81540715c4"},"references":{"count":25,"sample":[{"doi":"","year":1975,"title":"Statistical Theory of Reliability and Life Testing: Probability Models","work_id":"9c0aaa14-969a-41b9-ab6d-d832463b5fee","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Convexity and measures of statistical association","work_id":"d84fb24d-09b1-42e4-bbc9-1861be296eb8","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"B¨ ottcher, B., Keller-Ressel, M., Schilling, R. 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