Bio-equivalence tests in functional data by maximum deviation. (6th November 2020)

• Record Type: Journal Article
• Authors: Dette, Holger; Kokot, Kevin
• Is Part Of: Biometrika. Volume 108:Number 4(2021)
• Page Start: 895
• Page End: 913
• Publication Date: 2020-11-06
• Subjects: Banach space-valued random variable -- Bootstrap -- Equivalence test -- Functional data -- Maximum deviation -- Two-sample problem; Biometry -- Periodicals; 570.1519505
• DOI: 10.1093/biomet/asaa096
• Languages: English
• ISSNs: 0006-3444

Abstract

Summary: 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.