Wasserstein Projection Tests: Higher-Order Asymptotics and Connections to Empirical Likelihood

[2408.11753] Wasserstein Projection Tests: Higher-Order Asymptotics and Connections to Empirical Likelihood Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Statistics Theory arXiv:2408.11753 (math) [Submitted on 21 Aug 2024 ( v1 ), last revised 16 Aug 2026 (this version, v2)] Title: Wasserstein Projection Tests: Higher-Order Asymptotics and Connections to Empirical Likelihood Authors: Sirui Lin , Jose Blanchet , Peter Glynn , Viet Anh Nguyen View a PDF of the paper titled Wasserstein Projection Tests: Higher-Order Asymptotics and Connections to Empirical Likelihood, by Sirui Lin and 3 other authors View PDF HTML (experimental) Abstract: Tests of moment restrictions can be constructed by projecting the empirical distribution onto the set of laws satisfying the null. Wasserstein projection (WP) performs this projection by transporting mass in the sample space, rather than only reweighting observed atoms as in empirical likelihood (EL), and therefore incorporates both the ground geometry and the local variation of the moment function. Existing WP theory provides a first-order null limit but does not quantify finite-sample calibration or distinguish tests with the same limiting local power. We derive stochastic expansions of the rescaled WP statistic under the null and under Pitman-type local alternatives, identifying its order-$n^{-1/2}$ correction with a uniform remainder of order $\widetilde{O}_p(n^{-1})$. The resulting Edgeworth theory gives an order-$\widetilde{O}(n^{-1})$ size error for the plug-in WP test and an explicit order-$n^{-1/2}$ correction to local power. For scalar moments under local location shifts, WP, EL, and Hotelling's $T^2$ have the same first-order power, whereas their second-order ranking is determined by derivative-based curvature for WP and value-based skewness for EL. Extending the expansion by one further order, we construct two Bartlett-type corrections that improve coverage accuracy to $\widetilde{O}(n^{-3/2})$. Finally, we develop a certified localized dual algorithm that controls numerical error in the test decision. A theory-guided smooth fairness experiment using a common asymptotic chi-square reference quantile finds WP power gains over the corresponding EL and $T^2$ tests in the derivative-curvature regime predicted by the comparison theory. Comments: 115 pages. Revised version incorporating referee feedback: clarified the motivation, assumptions, and scope of the certified algorithm; expanded the technical discussion; improved notation and the proof roadmap; and added a code-availability statement with a reproducibility repository. Main theoretical results are unchanged Subjects: Statistics Theory (math.ST) ; Methodology (stat.ME) Cite as: arXiv:2408.11753 [math.ST] (or arXiv:2408.11753v2 [math.ST] for this version) https://doi.org/10.48550/arXiv.2408.11753 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Sirui Lin [ view email ] [v1] Wed, 21 Aug 2024 16:23:13 UTC (88 KB) [v2] Sun, 16 Aug 2026 09:31:25 UTC (494 KB) Full-text links: Access Paper: View a PDF of the paper titled Wasserstein Projection Tests: Higher-Order Asymptotics and Connections to Empirical Likelihood, by Sirui Lin and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.ST < prev | next > new | recent | 2024-08 Change to browse by: math stat stat.ME stat.TH References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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