{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T21:42:19Z","timestamp":1775857339367,"version":"3.50.1"},"reference-count":19,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2020,11,6]],"date-time":"2020-11-06T00:00:00Z","timestamp":1604620800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,11,15]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>We study the problem of testing equivalence of functional parameters, such as the mean or the variance function, in the two-sample functional data setting. In contrast to previous work where the functional problem is reduced to a multiple testing problem for the equivalence of scalar data by comparing the functions at each point, our approach is based on an estimate of a distance measuring the maximum deviation between the two functional parameters. Equivalence is claimed if the estimate for the maximum deviation does not exceed a given threshold. We propose a bootstrap procedure for obtaining quantiles of the distribution of the test statistic, and we prove consistency of the corresponding test in the large-sample scenario. As the methods proposed here avoid the use of the intersection-union principle, they are less conservative and more powerful than currently available approaches.<\/jats:p>","DOI":"10.1093\/biomet\/asaa096","type":"journal-article","created":{"date-parts":[[2020,10,28]],"date-time":"2020-10-28T04:20:15Z","timestamp":1603858815000},"page":"895-913","source":"Crossref","is-referenced-by-count":3,"title":["Bio-equivalence tests in functional data by maximum deviation"],"prefix":"10.1093","volume":"108","author":[{"given":"Holger","family":"Dette","sequence":"first","affiliation":[{"name":"Fakult\u00e4t f\u00fcr Mathematik, Ruhr-Universit\u00e4t Bochum, 44801 Bochum, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kevin","family":"Kokot","sequence":"additional","affiliation":[{"name":"Fakult\u00e4t f\u00fcr Mathematik, Ruhr-Universit\u00e4t Bochum, 44801 Bochum, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,11,6]]},"reference":[{"key":"2021111803494519500_B1","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1080\/01621459.2014.909317","article-title":"On the prediction of stationary functional time series","volume":"110","author":"Aue,","year":"2015","journal-title":"J. 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