Variable Selection for Multiple Function-on-Function Linear Regression
Xiong Cai,Liugen Xue,Jiguo Cao +2 more
TL;DR: In this paper, a variable selection procedure for function-on-function linear models with multiple functional predictors, using the functional principal component analysis (FPCA)-based estimation method with the group smoothly clipped absolute deviation regularization, is introduced.
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Abstract: We introduce a variable selection procedure for function-on-function linear models with multiple functional predictors, using the functional principal component analysis (FPCA)-based estimation method with the group smoothly clipped absolute deviation regularization. This approach enables us to select significant functional predictors and estimate the bivariate functional coefficients simultaneously. A datadriven procedure is provided for choosing the tuning parameters of the proposed method to achieve high efficiency. We construct FPCA-based estimators for the bivariate functional coefficients using the proposed regularization method. Under some mild conditions, we establish the estimation and selection consistencies of the proposed procedure. Simulation studies are carried out to illustrate the finite-sample performance of the proposed method. The results show that our method is highly effective in identifying the relevant functional predictors and in estimating the bivariate functional coefficients. Furthermore, the proposed method is demonstrated in a real-data example by investigating the association between ocean temperature and several water variables.
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Citations
Robust estimation and variable selection for function-on-scalar regression
Xiong Cai,Liugen Xue,Jiguo Cao +2 more
TL;DR: Cao et al. as mentioned in this paper developed a robust variable selection procedure for function-on-scalar regression with a large number of scalar predictors based on exponential squared loss combined with the group smoothly clipped absolute deviation regularization method.
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Sparse estimation of historical functional linear models with a nested group bridge approach
TL;DR: In this paper , the authors investigate the historical functional linear model with an unknown forward time lag into the history and propose an estimation procedure that uses the finite element method to conform naturally to the trapezoidal domain of the bivariate coefficient function.
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Sparse Estimation of Historical Functional Linear Models with a Nested Group Bridge Approach
Xiaolei Xun,Jiguo Cao +1 more
TL;DR: In this paper, the authors investigated the historical functional linear model with an unknown forward time lag into the history and proposed an estimation procedure adopting the finite element method to conform naturally to the trapezoidal domain of the bivariate coefficient function.
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FAStEN: an efficient adaptive method for feature selection and estimation in high-dimensional functional regressions
Tobia Boschi,Lorenzo Testa,Francesca Chiaromonte,Matthew Reimherr +3 more
- 26 Mar 2023
TL;DR: In this paper, a feature selection method for sparse high-dimensional function-on-function regression problem is proposed. But the method is limited to the scalar-on function framework.
The Second Wave of the COVID-19 Pandemic in Poland - Characterised Using FDA Methods
TL;DR: The author used the principal component analysis and multiple function-on-function linear regression model to predict the number of hospitalised and intensive care patients due to the COVID-19 infection during the second wave of the pandemic in Poland.
References
Shrinkage estimation and selection for multiple functional regression
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Estimating Truncated Functional Linear Models With a Nested Group Bridge Approach
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Sparse estimation for functional semiparametric additive models
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