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In particular, DRO with uncertainty set constructed as a statistical divergence neighborhood ball has been shown to provide a tool for constructing valid confidence intervals for nonparametric functionals and bears a duality with the empirical likelihood (EL). In this paper, we show how adjusting the ball size of such type of DRO can reduce higher-order coverage errors similar to the so-called Bartlett correction. Our correction, which applies to general von Mises differentiable functionals, is more general than the existing EL literature that only focuses on smooth function models or M-estimation. Moreover, we demonstrate a higher-order \u201cself-normalizing\u201d property of DRO regardless of the choice of divergence. Our approach builds on the development of a higher-order expansion of DRO, which is obtained through an asymptotic analysis on a fixed-point equation arising from the Karush-Kuhn-Tucker conditions.<\/jats:p>\n                  <jats:p>Funding: This work was supported by the National Science Foundation, Division of Information and Intelligent Systems [Grant IIS-1849280] and the Division of Civil, Mechanical and Manufacturing Innovation [Grant CAREER CMMI-1834710].<\/jats:p>","DOI":"10.1287\/moor.2023.0191","type":"journal-article","created":{"date-parts":[[2025,6,6]],"date-time":"2025-06-06T12:48:27Z","timestamp":1749214107000},"page":"1538-1584","source":"Crossref","is-referenced-by-count":0,"title":["Higher-Order Expansion and Bartlett Correctability of Distributionally Robust Optimization"],"prefix":"10.1287","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8521-8639","authenticated-orcid":false,"given":"Shengyi","family":"He","sequence":"first","affiliation":[{"name":"Department of Industrial Engineering & Operations Research, Columbia University, New York, New York 10027"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3193-563X","authenticated-orcid":false,"given":"Henry","family":"Lam","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering & Operations Research, Columbia University, New York, New York 10027"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"109","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1110.1011"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1137\/130939730"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/85.3.535"},{"issue":"901","key":"B4","first-page":"268","volume":"160","author":"Bartlett MS","year":"1937","journal-title":"Proc. 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