{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T04:04:11Z","timestamp":1751947451900,"version":"3.41.2"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,5,23]],"date-time":"2025-05-23T00:00:00Z","timestamp":1747958400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,5,23]],"date-time":"2025-05-23T00:00:00Z","timestamp":1747958400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2025,8]]},"DOI":"10.1007\/s11222-025-10634-6","type":"journal-article","created":{"date-parts":[[2025,5,23]],"date-time":"2025-05-23T13:34:23Z","timestamp":1748007263000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Two-armed Bandit Bootstrap for Model-free Equivalent Rank Test"],"prefix":"10.1007","volume":"35","author":[{"given":"Shuoxun","family":"Xu","sequence":"first","affiliation":[]},{"given":"Xiaodong","family":"Yan","sequence":"additional","affiliation":[]},{"given":"Zhaoang","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,5,23]]},"reference":[{"unstructured":"Bender, F., Douglass, L., Kramer, A.: Statistical methods for food and agriculture. (1982)","key":"10634_CR1"},{"issue":"4","key":"10634_CR2","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1214\/ss\/1032280304","volume":"11","author":"RL Berger","year":"1996","unstructured":"Berger, R.L., Hsu, J.C.: Bioequivalence trials, intersection-union tests and equivalence confidence sets. Statistical Science 11(4), 283\u2013319 (1996)","journal-title":"Statistical Science"},{"issue":"2","key":"10634_CR3","first-page":"123","volume":"24","author":"L Breiman","year":"1996","unstructured":"Breiman, L.: Bagging predictors. Machine learning 24(2), 123\u2013140 (1996)","journal-title":"Bagging predictors. Machine learning"},{"issue":"4","key":"10634_CR4","first-page":"927","volume":"30","author":"P B\u00fchlmann","year":"2002","unstructured":"B\u00fchlmann, P., Yu, B.: Analyzing bagging. The annals of. Statistics 30(4), 927\u2013961 (2002)","journal-title":"Statistics"},{"key":"10634_CR5","doi-asserted-by":"publisher","first-page":"424","DOI":"10.1016\/j.spa.2022.07.003","volume":"152","author":"Z Chen","year":"2022","unstructured":"Chen, Z., Epstein, L.G.: A central limit theorem for sets of probability measures. Stochastic Processes and their Applications 152, 424\u2013451 (2022)","journal-title":"Stochastic Processes and their Applications"},{"key":"10634_CR6","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1016\/j.neucom.2022.11.019","volume":"518","author":"Z Chen","year":"2023","unstructured":"Chen, Z., Feng, X., Liu, S., Yan, X.: Optimal distributions of rewards for a two-armed slot machine. Neurocomputing 518, 401\u2013407 (2023)","journal-title":"Neurocomputing"},{"unstructured":"Chen, Z., Feng, S., Zhang, G.: Strategy-driven limit theorems associated bandit problems. arXiv preprint arXiv:2204.04442 (2022)","key":"10634_CR7"},{"doi-asserted-by":"crossref","unstructured":"Chow, S.-C., Wang, H., Shao, J.: Sample size calculations in clinical research (2007)","key":"10634_CR8","DOI":"10.1201\/9781584889830"},{"unstructured":"Gretton, A., Sejdinovic, D., Strathmann, H., Balakrishnan, S., Pontil, M., Fukumizu, K., Sriperumbudur, B.K.: Optimal kernel choice for large-scale two-sample tests. Advances in neural information processing systems 25 (2012)","key":"10634_CR9"},{"issue":"7","key":"10634_CR10","doi-asserted-by":"publisher","first-page":"811","DOI":"10.1002\/sim.4780090710","volume":"9","author":"Y Hochberg","year":"1990","unstructured":"Hochberg, Y., Benjamini, Y.: More powerful procedures for multiple significance testing. Statistics in medicine 9(7), 811\u2013818 (1990)","journal-title":"Statistics in medicine"},{"doi-asserted-by":"crossref","unstructured":"ISIS-2 (Second International Study of Infarct Survival) Collaborative Group: Randomized trial of intravenous streptokinase, oral aspirin, both, or neither among 17,187 cases of suspected acute myocardial infarction: Isis-2. Journal of the American College of Cardiology 12(6SA), 3\u201313 (1988)","key":"10634_CR11","DOI":"10.1016\/0735-1097(88)92635-6"},{"issue":"1","key":"10634_CR12","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1524\/strm.2000.18.1.49","volume":"18","author":"A Janssen","year":"2000","unstructured":"Janssen, A.: Nonparametric bioequivalence tests for statistical functionals and their efficient power functions. Statistics & Risk Modeling 18(1), 49\u201378 (2000)","journal-title":"Statistics & Risk Modeling"},{"issue":"1","key":"10634_CR13","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1214\/aoms\/1177729080","volume":"24","author":"E Lehmann","year":"1953","unstructured":"Lehmann, E.: The power of rank tests. The Annals of Mathematical Statistics 24(1), 23\u201343 (1953)","journal-title":"The Annals of Mathematical Statistics"},{"unstructured":"Lopes, M., Jacob, L., Wainwright, M.J.: A more powerful two-sample test in high dimensions using random projection. Advances in Neural Information Processing Systems 24 (2011)","key":"10634_CR14"},{"issue":"2","key":"10634_CR15","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1177\/2515245918770963","volume":"1","author":"D Lakens","year":"2018","unstructured":"Lakens, D., Scheel, A.M., Isager, P.M.: Equivalence testing for psychological research: A tutorial. Advances in methods and practices in psychological science 1(2), 259\u2013269 (2018)","journal-title":"Advances in methods and practices in psychological science"},{"issue":"435","key":"10634_CR16","doi-asserted-by":"publisher","first-page":"1187","DOI":"10.1080\/01621459.1996.10476988","volume":"91","author":"A Munk","year":"1996","unstructured":"Munk, A.: Equivalence and interval testing for lehmann\u2019s alternative. Journal of the American Statistical Association 91(435), 1187\u20131196 (1996)","journal-title":"Journal of the American Statistical Association"},{"doi-asserted-by":"crossref","unstructured":"Mann, H.B., Whitney, D.R.: On a test of whether one of two random variables is stochastically larger than the other. The annals of mathematical statistics, 50\u201360 (1947)","key":"10634_CR17","DOI":"10.1214\/aoms\/1177730491"},{"doi-asserted-by":"crossref","unstructured":"Pearson, K.: X. on the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 50(302), 157\u2013175 (1900)","key":"10634_CR18","DOI":"10.1080\/14786440009463897"},{"unstructured":"Raj, N., Badcock, L., Brown, G., Deighton, C., O\u2019Reilly, S.: Education research (2003)","key":"10634_CR19"},{"issue":"3","key":"10634_CR20","doi-asserted-by":"publisher","first-page":"1036","DOI":"10.1214\/009053605000000048","volume":"33","author":"JP Romano","year":"2005","unstructured":"Romano, J.P.: Optimal testing of equivalence hypotheses. The Annals of Statistics 33(3), 1036\u20131047 (2005)","journal-title":"The Annals of Statistics"},{"doi-asserted-by":"crossref","unstructured":"Slivkins, A., et al.: Introduction to multi-armed bandits. Foundations and Trends\u00ae in Machine Learning 12(1-2), 1\u2013286 (2019)","key":"10634_CR21","DOI":"10.1561\/2200000068"},{"key":"10634_CR22","volume-title":"Reinforcement Learning: An Introduction","author":"RS Sutton","year":"2018","unstructured":"Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. MIT press, Cambridge, MA (2018)"},{"issue":"5","key":"10634_CR23","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1016\/j.biologicals.2011.06.014","volume":"39","author":"M Schiestl","year":"2011","unstructured":"Schiestl, M.: A biosimilar industry view on the implementation of the who guidelines on evaluating similar biotherapeutic products. Biologicals 39(5), 297\u2013299 (2011)","journal-title":"Biologicals"},{"issue":"2","key":"10634_CR24","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1214\/aoms\/1177730256","volume":"19","author":"N Smirnov","year":"1948","unstructured":"Smirnov, N.: Table for estimating the goodness of fit of empirical distributions. The annals of mathematical statistics 19(2), 279\u2013281 (1948)","journal-title":"The annals of mathematical statistics"},{"doi-asserted-by":"crossref","unstructured":"Student: The probable error of a mean. Biometrika, 1\u201325 (1908)","key":"10634_CR25","DOI":"10.2307\/2331554"},{"key":"10634_CR26","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/s11747-015-0455-4","volume":"44","author":"CM Voorhees","year":"2016","unstructured":"Voorhees, C.M., Brady, M.K., Calantone, R., Ramirez, E.: Discriminant validity testing in marketing: an analysis, causes for concern, and proposed remedies. Journal of the academy of marketing science 44, 119\u2013134 (2016)","journal-title":"Journal of the academy of marketing science"},{"issue":"1","key":"10634_CR27","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1002\/bimj.4710350105","volume":"35","author":"S Wellek","year":"1993","unstructured":"Wellek, S.: Basing the analysis of comparative bioavailability trials on an individualized statistical definition of equivalence. Biometrical journal 35(1), 47\u201355 (1993)","journal-title":"Biometrical journal"},{"issue":"6","key":"10634_CR28","doi-asserted-by":"publisher","first-page":"695","DOI":"10.1002\/bimj.4710380608","volume":"38","author":"S Wellek","year":"1996","unstructured":"Wellek, S.: A new approach to equivalence assessment in standard comparative bioavailability trials by means of the mann-whitney statistic. Biometrical journal 38(6), 695\u2013710 (1996)","journal-title":"Biometrical journal"},{"issue":"2","key":"10634_CR29","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1080\/10543406.2017.1397012","volume":"28","author":"D Zeng","year":"2018","unstructured":"Zeng, D., Pan, J., Hu, K., Chi, E., Lin, D.: Improving the power to establish clinical similarity in a phase 3 efficacy trial by incorporating prior evidence of analytical and pharmacokinetic similarity. Journal of biopharmaceutical statistics 28(2), 320\u2013332 (2018)","journal-title":"Journal of biopharmaceutical statistics"},{"key":"10634_CR30","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2021.107318","volume":"164","author":"H Zhang","year":"2021","unstructured":"Zhang, H., Wang, H.: A more powerful test of equality of high-dimensional two-sample means. Computational Statistics & Data Analysis 164, 107318 (2021)","journal-title":"Computational Statistics & Data Analysis"}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-025-10634-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11222-025-10634-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-025-10634-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T05:30:17Z","timestamp":1751866217000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11222-025-10634-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,23]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,8]]}},"alternative-id":["10634"],"URL":"https:\/\/doi.org\/10.1007\/s11222-025-10634-6","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"type":"print","value":"0960-3174"},{"type":"electronic","value":"1573-1375"}],"subject":[],"published":{"date-parts":[[2025,5,23]]},"assertion":[{"value":"21 August 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 May 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 May 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 July 2025","order":4,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Update","order":5,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Conflict of interest statement updated.","order":6,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Xiaodong Yan was supported by the National Key R&D Program of China (No. 2023YFA1008701) and National Natural Science Foundation of China (No. 12371292) equally.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}}],"article-number":"102"}}