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.
read more
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.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
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.
6
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.
•Posted Content
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.
1
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
Regression Shrinkage and Selection via the Lasso
TL;DR: A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.
Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
Jianqing Fan,Runze Li +1 more
TL;DR: In this article, penalized likelihood approaches are proposed to handle variable selection problems, and it is shown that the newly proposed estimators perform as well as the oracle procedure in variable selection; namely, they work as well if the correct submodel were known.
Nearly unbiased variable selection under minimax concave penalty
TL;DR: It is proved that at a universal penalty level, the MC+ has high probability of matching the signs of the unknowns, and thus correct selection, without assuming the strong irrepresentable condition required by the LASSO.
3.8K
Functional Data Analysis
TL;DR: In this article, the authors provide an overview of FDA, starting with simple statistical notions such as mean and covariance functions, then covering some core techniques, the most popular of which is functional principal component analysis (FPCA).
Pathwise coordinate optimization
TL;DR: It is shown that coordinate descent is very competitive with the well-known LARS procedure in large lasso problems, can deliver a path of solutions efficiently, and can be applied to many other convex statistical problems such as the garotte and elastic net.
2.3K