The interval testing procedure: A general framework for inference in functional data analysis. We introduce in this work the Interval Testing Procedure (ITP), a novel inferential technique for functional data. The procedure can be used to test different functional hypotheses, e.g., distributional equality between two or more functional populations, equality of mean function of a functional population to a reference. ITP involves three steps: (i) the representation of data on a (possibly high-dimensional) functional basis; (ii) the test of each possible set of consecutive basis coefficients; (iii) the computation of the adjusted $p$-values associated to each basis component, by means of a new strategy here proposed. We define a new type of error control, the interval-wise control of the family wise error rate, particularly suited for functional data. We show that ITP is provided with such a control. A simulation study comparing ITP with other testing procedures is reported. ITP is then applied to the analysis of hemodynamical features involved with cerebral aneurysm pathology. ITP is implemented in the fdatest R package.

References in zbMATH (referenced in 13 articles , 1 standard article )

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  1. Qiu, Zhiping; Chen, Jianwei; Zhang, Jin-Ting: Two-sample tests for multivariate functional data with applications (2021)
  2. Valeria Policastro, Dario Righelli, Annamaria Carissimo, Luisa Cutillo, Italia De Feis: ROBustness In Network (robin): an R package for Comparison and Validation of communities (2021) arXiv
  3. Aneiros, Germán; Cao, Ricardo; Fraiman, Ricardo; Genest, Christian; Vieu, Philippe: Recent advances in functional data analysis and high-dimensional statistics (2019)
  4. Kraus, David: Inferential procedures for partially observed functional data (2019)
  5. Pini, Alessia; Spreafico, Lorenzo; Vantini, Simone; Vietti, Alessandro: Multi-aspect local inference for functional data: analysis of ultrasound tongue profiles (2019)
  6. Sharghi, Ghale-Joogh Hassan: Statistical inference for functional data: two sample Behrens-Fisher problem (2019)
  7. Abramowicz, Konrad; Häger, Charlotte K.; Pini, Alessia; Schelin, Lina; de Luna, Sara Sjöstedt; Vantini, Simone: Nonparametric inference for functional-on-scalar linear models applied to knee kinematic hop data after injury of the anterior cruciate ligament (2018)
  8. Carissimo, Annamaria; Cutillo, Luisa; Feis, Italia De: Validation of community robustness (2018)
  9. Pini, Alessia; Stamm, Aymeric; Vantini, Simone: Hotelling’s (T^2) in separable Hilbert spaces (2018)
  10. Sharghi Ghale-Joogh, Hassan; Hosseini-Nasab, S. Mohammad E.: A two-sample test for mean functions with increasing number of projections (2018)
  11. Ghiglietti, Andrea; Ieva, Francesca; Paganoni, Anna Maria: Statistical inference for stochastic processes: two-sample hypothesis tests (2017)
  12. Paganoni, Anna Maria; Sangalli, Laura M.: Functional regression models: some directions of future research (2017)
  13. Pini, Alessia; Vantini, Simone: The interval testing procedure: a general framework for inference in functional data analysis (2016)