{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T04:50:09Z","timestamp":1791435009581,"version":"4.3.3"},"reference-count":27,"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":"Across science and policy, decision-makers often need to draw conclusions about the best candidate among competing alternatives. For instance, researchers may seek to infer the effectiveness of the most successful treatment or determine which demographic group benefits most from a specific treatment. Similarly, in machine learning, practitioners are often interested in the population performance of the model that performs best empirically. However, cherry-picking the best candidate leads to the winner\u2019s curse: the observed performance for the winner is biased upwards, rendering conclusions based on standard measures of uncertainty invalid. We introduce the zoom correction, a novel approach for valid inference on the winner. Our method is flexible: it can be employed in both parametric and nonparametric settings, can handle arbitrary dependencies between candidates, and automatically adapts to the level of selection bias. The method easily extends to important related problems, such as inference on the top k winners, inference on the value and identity of the population winner, and inference on \u201cnear-winners.\u201d<\/jats:p>","DOI":"10.1214\/25-aos2553","type":"journal-article","created":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T06:15:31Z","timestamp":1766470531000},"page":"2516-2535","source":"Crossref","is-referenced-by-count":1,"title":["A flexible defense against the winner\u2019s curse"],"prefix":"10.1214","volume":"53","author":[{"given":"Tijana","family":"Zrnic","sequence":"first","affiliation":[{"name":"Stanford Data Science & Department of Statistics, Stanford University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"William","family":"Fithian","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of California, Berkeley"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"4","doi-asserted-by":"publisher","unstructured":"Bradley, R. A.<\/small> and Terry, M. E.<\/small> (1952). Rank analysis of incomplete block designs. I. The method of paired comparisons. Biometrika<\/i> 39<\/b> 324\u2013345.","DOI":"10.2307\/2334029"},{"key":"12","doi-asserted-by":"publisher","unstructured":"KIVARANOVIC, D.<\/small> and LEEB, H.<\/small> (2021). On the length of post-model-selection confidence intervals conditional on polyhedral constraints. J. Amer. Statist. Assoc.<\/i> 116<\/b> 845\u2013857.","DOI":"10.1080\/01621459.2020.1732989"},{"key":"19","doi-asserted-by":"publisher","unstructured":"RASINES, D. G.<\/small> and YOUNG, G. A.<\/small> (2023). Splitting strategies for post-selection inference. Biometrika<\/i> 110<\/b> 597\u2013614.","DOI":"10.1093\/biomet\/asac070"},{"key":"13","doi-asserted-by":"publisher","unstructured":"Lee, J. D.<\/small>, Sun, D. L.<\/small>, Sun, Y.<\/small> and Taylor, J. E.<\/small> (2016). Exact post-selection inference, with application to the lasso. Ann. Statist.<\/i> 44<\/b> 907\u2013927.","DOI":"10.1214\/15-AOS1371"},{"key":"21","doi-asserted-by":"publisher","unstructured":"Tian, X.<\/small> and Taylor, J.<\/small> (2018). Selective inference with a randomized response. Ann. Statist.<\/i> 46<\/b> 679\u2013710.","DOI":"10.1214\/17-AOS1564"},{"key":"7","doi-asserted-by":"crossref","unstructured":"Deng, J.<\/small>, Dong, W.<\/small>, Socher, R.<\/small>, Li, L.-J.<\/small>, Li, K.<\/small> and Fei-Fei, L.<\/small> (2009). Imagenet: A large-scale hierarchical image database. In 2009 IEEE Conference on Computer Vision and Pattern Recognition<\/i> 248\u2013255. IEEE.","DOI":"10.1109\/CVPR.2009.5206848"},{"key":"27","doi-asserted-by":"publisher","unstructured":"ZRNIC, T.<\/small> and JORDAN, M. I.<\/small> (2023). Post-selection inference via algorithmic stability. Ann. Statist.<\/i> 51<\/b> 1666\u20131691.","DOI":"10.1214\/23-aos2303"},{"key":"2","doi-asserted-by":"crossref","unstructured":"ANDREWS, I.<\/small>, KITAGAWA, T.<\/small> and MCCLOSKEY, A.<\/small> (2024). Inference on winners. Q. J. Econ.<\/i> 139<\/b> 305\u2013358.","DOI":"10.1093\/qje\/qjad043"},{"key":"8","doi-asserted-by":"publisher","unstructured":"DICKHAUS, T.<\/small> (2014). Simultaneous Statistical Inference<\/i>: With Applications in the Life Sciences<\/i>. Springer, Heidelberg.","DOI":"10.1007\/978-3-642-45182-9"},{"key":"10","doi-asserted-by":"publisher","unstructured":"FUENTES, C.<\/small>, CASELLA, G.<\/small> and WELLS, M. T.<\/small> (2018). Confidence intervals for the means of the selected populations. Electron. J. Stat.<\/i> 12<\/b> 58\u201379.","DOI":"10.1214\/17-EJS1374"},{"key":"20","doi-asserted-by":"crossref","unstructured":"RASP, S.<\/small>, DUEBEN, P. D.<\/small>, SCHER, S.<\/small>, WEYN, J. A.<\/small>, MOUATADID, S.<\/small> and THUEREY, N.<\/small> (2020). WeatherBench: A benchmark data set for data-driven weather forecasting. J. Adv. Model. Earth Syst.<\/i> 12<\/b> e2020MS002203.","DOI":"10.1029\/2020MS002203"},{"key":"23","unstructured":"VENTER, J.<\/small> (1988). Confidence bounds based on the largest treatment mean. South Afr. J. Sci.<\/i> 84<\/b> 340."},{"key":"9","unstructured":"FITHIAN, W.<\/small>, SUN, D.<\/small> and TAYLOR, J.<\/small> (2014). Optimal inference after model selection. Preprint. Available at arXiv:1410.2597<\/a>."},{"key":"14","doi-asserted-by":"publisher","unstructured":"LEINER, J.<\/small>, DUAN, B.<\/small>, WASSERMAN, L.<\/small> and RAMDAS, A.<\/small> (2025). Data fission: Splitting a single data point. J. Amer. Statist. Assoc.<\/i> 120<\/b> 135\u2013146.","DOI":"10.1080\/01621459.2023.2270748"},{"key":"1","doi-asserted-by":"crossref","unstructured":"ANDREWS, I.<\/small>, BOWEN, D.<\/small>, KITAGAWA, T.<\/small> and MCCLOSKEY, A.<\/small> (2022). Inference for losers. In AEA Papers and Proceedings<\/i> 112<\/b> 635\u2013640. American Economic Association.","DOI":"10.1257\/pandp.20221065"},{"key":"3","unstructured":"BENJAMINI, Y.<\/small>, HECHTLINGER, Y.<\/small> and STARK, P. B.<\/small> (2019). Confidence intervals for selected parameters. Preprint. Available at arXiv:1906.00505<\/a>."},{"key":"5","unstructured":"CHIANG, W.-L.<\/small>, ZHENG, L.<\/small>, SHENG, Y.<\/small>, ANGELOPOULOS, A. N.<\/small>, LI, T.<\/small>, LI, D.<\/small>, ZHU, B.<\/small>, ZHANG, H.<\/small>, JORDAN, M.<\/small> et al. (2024). Chatbot arena: An open platform for evaluating LLMs by human preference. In Forty-First International Conference on Machine Learning<\/i>."},{"key":"6","unstructured":"DANESCU-NICULESCU-MIZIL, C.<\/small>, SUDHOF, M.<\/small>, JURAFSKY, D.<\/small>, LESKOVEC, J.<\/small> and POTTS, C.<\/small> (2013). A computational approach to politeness with application to social factors. In 51st Annual Meeting of the Association for Computational Linguistics<\/i> 250\u2013259. ACL."},{"key":"11","doi-asserted-by":"publisher","unstructured":"HUNG, K.<\/small> and FITHIAN, W.<\/small> (2019). Rank verification for exponential families. Ann. Statist.<\/i> 47<\/b> 758\u2013782.","DOI":"10.1214\/17-AOS1634"},{"key":"15","doi-asserted-by":"crossref","unstructured":"MILLER, R. G. JR.<\/small> (1981). Simultaneous Statistical Inference<\/i>, 2nd ed. Springer Series in Statistics<\/i>. Springer, New York.","DOI":"10.1007\/978-1-4613-8122-8"},{"key":"16","doi-asserted-by":"crossref","unstructured":"MOGSTAD, M.<\/small>, ROMANO, J. P.<\/small>, SHAIKH, A. M.<\/small> and WILHELM, D.<\/small> (2024). Inference for ranks with applications to mobility across neighbourhoods and academic achievement across countries. Rev. Econ. Stud.<\/i> 91<\/b> 476\u2013518.","DOI":"10.1093\/restud\/rdad006"},{"key":"17","unstructured":"NEUFELD, A.<\/small>, DHARAMSHI, A.<\/small>, GAO, L. L.<\/small> and WITTEN, D.<\/small> (2024). Data thinning for convolution-closed distributions. J. Mach. Learn. Res.<\/i> 25<\/b> Paper No. [57], 35."},{"key":"18","unstructured":"PERRY, R.<\/small>, XU, Z.<\/small>, MCGOUGH, O.<\/small> and WITTEN, D.<\/small> (2024). Infer-and-widen versus split-and-condition: Two tales of selective inference. Preprint. Available at arXiv:2408.06323<\/a>."},{"key":"22","unstructured":"TORCHVISION MAINTAINERS AND CONTRIBUTORS<\/small> (2016). TorchVision: PyTorch\u2019s Computer Vision library. https:\/\/github.com\/pytorch\/vision<\/a>. GitHub repository."},{"key":"24","doi-asserted-by":"publisher","unstructured":"ZRNIC, T.<\/small> and FITHIAN, W.<\/small> (2024). Locally simultaneous inference. Ann. Statist.<\/i> 52<\/b> 1227\u20131253.","DOI":"10.1214\/24-aos2391"},{"key":"25","doi-asserted-by":"crossref","unstructured":"ZRNIC, T.<\/small> and FITHIAN, W.<\/small> (2025). Supplement to \u201cA flexible defense against the winner\u2019s curse.\u201d https:\/\/doi.org\/10.1214\/25-AOS2553SUPP<\/a>","DOI":"10.1214\/25-AOS2553SUPP"},{"key":"26","doi-asserted-by":"crossref","unstructured":"ZRNIC, T.<\/small> and FITHIAN, W.<\/small> (2025). A flexible defense against the winner\u2019s curse: Code.","DOI":"10.1214\/25-AOS2553"}],"container-title":["The Annals of Statistics"],"original-title":[],"deposited":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T16:22:40Z","timestamp":1791390160000},"score":1,"resource":{"primary":{"URL":"https:\/\/projecteuclid.org\/journals\/annals-of-statistics\/volume-53\/issue-6\/A-flexible-defense-against-the-winners-curse\/10.1214\/25-AOS2553.full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,1]]},"references-count":27,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,12,1]]}},"URL":"https:\/\/doi.org\/10.1214\/25-aos2553","relation":{},"ISSN":["0090-5364","2168-8966"],"issn-type":[{"value":"0090-5364","type":"print"},{"value":"2168-8966","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,1]]}}}