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- Abramowicz, Konrad,1983-Umeå universitet,Institutionen för matematik och matematisk statistik (author)
Domain selection and family-wise error rate for functional data : a unified framework
- Article/chapterEnglish2023
Publisher, publication year, extent ...
- 2022-04-25
- John Wiley & Sons,2023
- electronicrdacarrier
Numbers
- LIBRIS-ID:oai:DiVA.org:umu-193740
- https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-193740URI
- https://doi.org/10.1111/biom.13669DOI
Supplementary language notes
- Language:English
- Summary in:English
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- SwePubSwePub
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Notes
- First published online: 30 March 2022
- Functional data are smooth, often continuous, random curves, which can be seen as an extreme case of multivariate data with infinite dimensionality. Just as component-wise inference for multivariate data naturally performs feature selection, subset-wise inference for functional data performs domain selection. In this paper, we present a unified testing framework for domain selection on populations of functional data. In detail, p-values of hypothesis tests performed on point-wise evaluations of functional data are suitably adjusted for providing a control of the family-wise error rate (FWER) over a family of subsets of the domain. We show that several state-of-the-art domain selection methods fit within this framework and differ from each other by the choice of the family over which the control of the FWER is provided. In the existing literature, these families are always defined a priori. In this work, we also propose a novel approach, coined threshold-wise testing, in which the family of subsets is instead built in a data-driven fashion. The method seamlessly generalizes to multidimensional domains in contrast to methods based on a-priori defined families. We provide theoretical results with respect to consistency and control of the FWER for the methods within the unified framework. We illustrate the performance of the methods within the unified framework on simulated and real data examples, and compare their performance with other existing methods.
Subject headings and genre
- NATURVETENSKAP Matematik Sannolikhetsteori och statistik hsv//swe
- NATURAL SCIENCES Mathematics Probability Theory and Statistics hsv//eng
- adjusted p-value function
- functional data
- local inference
- permutation test
- Statistics
- statistik
Added entries (persons, corporate bodies, meetings, titles ...)
- Pini, AlessiaDepartment of Statistical Sciences, Università Cattolica del Sacro Cuore, Milan, Italy (author)
- Schelin, LinaUmeå universitet,Statistik(Swepub:umu)lnalug02 (author)
- Sjöstedt de Luna, Sara,1964-Umeå universitet,Institutionen för matematik och matematisk statistik(Swepub:umu)sade0001 (author)
- Stamm, AymericDepartment of Mathematics Jean Leray, UMR CNRS 6629, Nantes University, Nantes, France (author)
- Vantini, SimoneMOX – Modelling and Scientific Computing Laboratory, Department of Mathematics, Politecnico di Milano, Milan, Italy (author)
- Umeå universitetInstitutionen för matematik och matematisk statistik (creator_code:org_t)
Related titles
- In:Biometrics: John Wiley & Sons79:2, s. 1119-11320006-341X1541-0420
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