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2021). Covariance-based low-dimensional registration for function-on-function regression. Stat, 10( 1), e404. https://doi.org/10.1002/sta4.404, , , & (
Functional data analysis (FDA) has established itself as an important and dynamic area of statistics, and it presents several open and fascinating theoretical and computational challenges. In FDA data are represented as curves – i.e. infinite-dimensional objects which must be estimated from a finite sample by imposing smoothness conditions. Just as in the classical framework, Linear Regression is one of the most fundamental tools in FDA. In particular, the authors focus on function-on-function regression, where a functional response is regressed against a functional predictor. In this context, they propose a new low-dimensional registration procedure that exploits the relationship between response and predictor. This kind of registration aims to improve the regression performance by horizontally shifting and dilating each curve according to targets that capture information relevant to the model. Given the importance and the broad use of regression models, the method presented in this paper offers a new effective tool applicable to domain sciences such as medicine, physics, business, and engineering. In particular, the efficacy of the novel registration procedure is demonstrated through simulations and an analysis of the AneuRisk dataset. The AneuRisk project investigates the interplay between morphological properties of artery walls and hemodynamic factors — shedding light on the possible causes of aneurysmal pathology. In particular, in this paper, the authors study the relationship between the curvature and the wall shear stress of the internal carotid artery.