{"paper":{"title":"Transformations and Hardy-Krause variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"stat.CO","authors_text":"Art B. Owen, Kinjal Basu","submitted_at":"2015-12-09T01:28:00Z","abstract_excerpt":"Using a multivariable Faa di Bruno formula we give conditions on transformations $\\tau:[0,1]^m\\to\\mathcal{X}$ where $\\mathcal{X}$ is a closed and bounded subset of $\\mathbb{R}^d$ such that $f\\circ\\tau$ is of bounded variation in the sense of Hardy and Krause for all $f\\in C^d(\\mathcal{x})$. We give similar conditions for $f\\circ\\tau$ to be smooth enough for scrambled net sampling to attain $O(n^{-3/2+\\epsilon})$ accuracy. Some popular symmetric transformations to the simplex and sphere are shown to satisfy neither condition. Some other transformations due to Fang and Wang (1993) satisfy the fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02713","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"}