{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T16:57:09Z","timestamp":1791392229684,"version":"4.3.3"},"reference-count":87,"publisher":"Institute of Mathematical Statistics","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann. Statist."],"published-print":{"date-parts":[[2025,12,1]]},"abstract":"<jats:p>Semi-supervised datasets are ubiquitous across diverse domains where obtaining fully labeled data is costly or time-consuming. The prevalence of such datasets has consistently driven the demand for new tools and methods that exploit the potential of unlabeled data. Responding to this demand, we introduce semi-supervised U-statistics enhanced by the abundance of unlabeled data, and investigate their statistical properties. We show that the proposed approach is asymptotically Normal and exhibits notable efficiency gains over classical U-statistics by effectively integrating various powerful prediction tools into the framework. To understand the fundamental difficulty of the problem, we derive minimax lower bounds in semi-supervised settings and showcase that our procedure is semi-parametrically efficient under regularity conditions. Moreover, tailored to bivariate kernels, we propose a refined approach that outperforms the classical U-statistic across all degeneracy regimes, and demonstrate its optimality properties. Simulation studies are conducted to corroborate our findings and to further demonstrate our framework.<\/jats:p>","DOI":"10.1214\/25-aos2550","type":"journal-article","created":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T06:15:19Z","timestamp":1766470519000},"page":"2488-2515","source":"Crossref","is-referenced-by-count":0,"title":["Semi-supervised U-statistics"],"prefix":"10.1214","volume":"53","author":[{"given":"Ilmun","family":"Kim","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, KAIST"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Larry","family":"Wasserman","sequence":"additional","affiliation":[{"name":"Department of Statistics and Data Science, Carnegie Mellon University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sivaraman","family":"Balakrishnan","sequence":"additional","affiliation":[{"name":"Department of Statistics and Data Science, Carnegie Mellon University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matey","family":"Neykov","sequence":"additional","affiliation":[{"name":"Department of Statistics and Data Science, Northwestern University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"22","doi-asserted-by":"crossref","unstructured":"<small>Chen, T.<\/small> and <small>Guestrin, C.<\/small> (2016). 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