{"paper":{"title":"Distributionally Robust Optimization with Confidence Bands for Probability Density Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Guanglin Xu, Qihang Lin, Xi Chen","submitted_at":"2019-01-08T06:16:02Z","abstract_excerpt":"Distributionally robust optimization (DRO) has been introduced for solving stochastic programs where the distribution of the random parameters is unknown and must be estimated by samples from that distribution. A key element of DRO is the construction of the ambiguity set, which is a set of distributions that covers the true distribution with a high probability. Assuming that the true distribution has a probability density function, we propose a class of ambiguity sets based on confidence bands of the true density function. The use of the confidence band enables us to take the prior knowledge "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02169","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"}