Adaptive smoothing spline estimator for the function-on-function linear regression model

@article{Centofanti2022AdaptiveSS,
  title={Adaptive smoothing spline estimator for the function-on-function linear regression model},
  author={Fabio Centofanti and Antonio Lepore and Alessandra Menafoglio and Biagio Palumbo and Simone Vantini},
  journal={Computational Statistics},
  year={2022}
}
In this paper, we propose an adaptive smoothing spline (AdaSS) estimator for the function-on-function linear regression model where each value of the response, at any domain point, depends on the full trajectory of the predictor. The AdaSS estimator is obtained by the optimization of an objective function with two spatially adaptive penalties, based on initial estimates of the partial derivatives of the regression coefficient function. This allows the proposed estimator to adapt more easily to… 
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References

SHOWING 1-10 OF 54 REFERENCES
Smoothing splines with varying smoothing parameter
This paper considers the development of spatially adaptive smoothing splines for the estimation of a regression function with nonhomogeneous smoothness across the domain. Two challenging issues
Theory & Methods: Spatially‐adaptive Penalties for Spline Fitting
The paper studies spline fitting with a roughness penalty that adapts to spatial heterogeneity in the regression function. The estimates are pth degree piecewise polynomials with p− 1 continuous
SPLINE ESTIMATORS FOR THE FUNCTIONAL LINEAR MODEL
TLDR
This work considers a regression setting where the response is a scalar and the predictor is a random function defined on a compact set of R, and studies an estimator based on a B-splines expansion of the functional coefficient which generalizes ridge regression.
Nonlinear function on function additive model with multiple predictor curves
We consider a nonlinear function-on-function additive regression model with multiple functional predictors. The forms of the nonlinear functions are unspecified, and offer great flexibility to model
A Locally Adaptive Penalty for Estimation of Functions With Varying Roughness
TLDR
The Loco-Spline substantially outperforms the traditional smoothing spline and the locally adaptive kernel smoother and achieves optimal MSE rate of convergence in a simulation study.
Generalized functional linear models
We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained
Generalized functional linear models
We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained
Locally Sparse Estimator for Functional Linear Regression Models
ABSTRACT A new locally sparse (i.e., zero on some subregions) estimator for coefficient functions in functional linear regression models is developed based on a novel functional regularization
Function-on-Function Linear Regression by Signal Compression
ABSTRACT We consider functional linear regression models with a functional response and multiple functional predictors, with the goal of finding the best finite-dimensional approximation to the
Interaction Model and Model Selection for Function-on-Function Regression
  • Ruiyan Luo, Xin Qi
  • Mathematics
    Journal of Computational and Graphical Statistics
  • 2019
Abstract Regression models with interaction effects have been widely used in multivariate analysis to improve model flexibility and prediction accuracy. In functional data analysis, however, due to
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