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Nonparametric inference for functional‐on‐scalar linear models applied to knee kinematic hop data after injury of the anterior cruciate ligament

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  • Konrad Abramowicz
  • Charlotte K. Häger
  • Alessia Pini
  • Lina Schelin
  • Sara Sjöstedt de Luna
  • Simone Vantini

Abstract

Motivated by the analysis of the dependence of knee movement patterns during functional tasks on subject‐specific covariates, we introduce a distribution‐free procedure for testing a functional‐on‐scalar linear model with fixed effects. The procedure does not only test the global hypothesis on the entire domain but also selects the intervals where statistically significant effects are detected. We prove that the proposed tests are provided with an asymptotic control of the intervalwise error rate, that is, the probability of falsely rejecting any interval of true null hypotheses. The procedure is applied to one‐leg hop data from a study on anterior cruciate ligament injury. We compare knee kinematics of three groups of individuals (two injured groups with different treatments and one group of healthy controls), taking individual‐specific covariates into account.

Suggested Citation

  • Konrad Abramowicz & Charlotte K. Häger & Alessia Pini & Lina Schelin & Sara Sjöstedt de Luna & Simone Vantini, 2018. "Nonparametric inference for functional‐on‐scalar linear models applied to knee kinematic hop data after injury of the anterior cruciate ligament," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(4), pages 1036-1061, December.
    • Handle: RePEc:bla:scjsta:v:45:y:2018:i:4:p:1036-1061
    DOI: 10.1111/sjos.12333
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    Citations

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    1. Niels Lundtorp Olsen & Alessia Pini & Simone Vantini, 2021. "False discovery rate for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 784-809, September.
    2. Římalová, Veronika & Fišerová, Eva & Menafoglio, Alessandra & Pini, Alessia, 2022. "Inference for spatial regression models with functional response using a permutational approach," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Agostino Torti & Alessia Pini & Simone Vantini, 2021. "Modelling time‐varying mobility flows using function‐on‐function regression: Analysis of a bike sharing system in the city of Milan," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(1), pages 226-247, January.
    4. Todd Colin Pataky & Konrad Abramowicz & Dominik Liebl & Alessia Pini & Sara Sjöstedt Luna & Lina Schelin, 2023. "Simultaneous inference for functional data in sports biomechanics," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(1), pages 369-392, March.
    5. Pini, Alessia & Sørensen, Helle & Tolver, Anders & Vantini, Simone, 2023. "Local inference for functional linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    6. Centofanti, Fabio & Fontana, Matteo & Lepore, Antonio & Vantini, Simone, 2022. "Smooth LASSO estimator for the Function-on-Function linear regression model," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    7. Pini, Alessia & Spreafico, Lorenzo & Vantini, Simone & Vietti, Alessandro, 2019. "Multi-aspect local inference for functional data: Analysis of ultrasound tongue profiles," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 162-185.
    8. Matteo Fontana & Massimo Tavoni & Simone Vantini, 2020. "Global Sensitivity and Domain-Selective Testing for Functional-Valued Responses: An Application to Climate Economy Models," Papers 2006.13850, arXiv.org, revised Apr 2024.
    9. Konrad Abramowicz & Alessia Pini & Lina Schelin & Sara Sjöstedt de Luna & Aymeric Stamm & Simone Vantini, 2023. "Domain selection and familywise error rate for functional data: A unified framework," Biometrics, The International Biometric Society, vol. 79(2), pages 1119-1132, June.
    10. Matteo Fontana & Massimo Tavoni & Simone Vantini, 2019. "Functional Data Analysis of high-frequency load curves reveals drivers of residential electricity consumption," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-16, June.
    11. Veronika Římalová & Alessandra Menafoglio & Alessia Pini & Vilém Pechanec & Eva Fišerová, 2020. "A permutation approach to the analysis of spatiotemporal geochemical data in the presence of heteroscedasticity," Environmetrics, John Wiley & Sons, Ltd., vol. 31(4), June.

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