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Nonparametric functional concurrent regression models

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Function‐on‐function regression refers to the situation where both independent and dependent variables in a regression model are of functional nature. Functional concurrent regression is a specific type of function‐on‐function regression that relates the response function at a specific point to the covariate value at that point and the point itself. Standard functional concurrent models are linear (a linear combination of the covariates is used), and often criticized due to their linearity assumption and lack of flexibility. This gives rise to nonparametric functional concurrent regression that models the response function at a specific point using a multivariate nonparametric function of both the point and the covariate value at that point. Such models allow for much more flexibility and predictive accuracy, especially when the underlying relationship is nonlinear. In the past decade, several methods have been proposed to perform estimation, prediction and inference in the nonparametric concurrent models using various methods such as spline smoothing, Gaussian process regression and local polynomial kernel regression. Such models have been shown to be useful tools in functional regression as well as stepping stone for further development. WIREs Comput Stat 2017, 9:e1394. doi: 10.1002/wics.1394 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Nonparametric Methods
Results from gait data analysis. The first row displays the observed hip (left panel) and knee angles (middle panel), and the out‐of‐sample root mean squared prediction errors (right panel) of the three methods. The bottom row displays the full estimated bivariate surfaces using spline (left panel), Gaussian process (middle panel), and kernel smoothing (right panel) based methods, respectively.
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Statistical and Graphical Methods of Data Analysis > Nonparametric Methods

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