{"paper":{"title":"Convergence in distribution norms in the CLT for non identical distributed random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guillaume Poly, Lucia Caramellino, Vlad Bally","submitted_at":"2016-06-06T06:38:55Z","abstract_excerpt":"We study the convergence in distribution norms in the Central Limit Theorem for non identical distributed random variables that is $$ \\varepsilon_{n}(f):={\\mathbb{E}}\\Big(f\\Big(\\frac 1{\\sqrt n}\\sum_{i=1}^{n}Z_{i}\\Big)\\Big)-{\\mathbb{E}}\\big(f(G)\\big)\\rightarrow 0 $$ where $Z_{i}$ are centred independent random variables and $G$ is a Gaussian random variable. We also consider local developments (Edgeworth expansion). This kind of results is well understood in the case of smooth test functions $f$. If one deals with measurable and bounded test functions (convergence in total variation distance), "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01629","kind":"arxiv","version":3},"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"}