{"paper":{"title":"Double asymptotics for the chi-square statistic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Grzegorz A. Rempa{\\l}a, Jacek Weso{\\l}owski","submitted_at":"2016-09-10T14:36:13Z","abstract_excerpt":"We consider distributional limit of the Pearson chi-square statistic when the number of classes m increases with the sample size n in such way that $n/\\sqrt{m} \\to {\\lambda}$. Under mild moment conditions, the limit is Gaussian for ${\\lambda} = \\infty$, Poisson for finite ${\\lambda} > 0$, and degenerate for ${\\lambda} = 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03060","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"}