Sparse estimation in functional linear regression

Lee, Eun Ryung; Park, Byeong U.

doi:10.1016/j.jmva.2011.08.005

Cited by 39 publications

(23 citation statements)

References 22 publications

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“…In addition, let ζ H n = min h∈H n |β h | be the smallest magnitude of the coefficients. Following Lee and Park (2012), who proposed a general framework for penalized least squared estimation of η in Equation (1), we make the following assumptions:…”

Section: Consistent Estimationmentioning

confidence: 99%

“…The literature on functional linear regression is growing. A sampling of papers examining this situation and various asymptotic properties includes Cardot, Ferraty, and Sarda (2003), Cardot and Sarda (2005), Cai and Hall (2006), Antoniadis and Sapatinas (2007), Hall and Horowitz (2007), Li and Hsing (2007), Reiss and Ogden (2007), Müller and Yao (2008), Crainiceanu, Staicu, and Di (2009), Delaigle, Hall, and Apanasovich (2009), James, Wang, and Zhu (2009), Crambes, Kneip, and Sarda (2009), Goldsmith et al (2012), and Lee and Park (2012). A potentially very useful idea in fitting models involving functional data is to transform functional data via wavelets.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Wavelet-Based Weighted LASSO and Screening Approaches in Functional Linear Regression

Zhao¹,

Chen²,

Ogden³

2015

Journal of Computational and Graphical Statistics

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One useful approach for fitting linear models with scalar outcomes and functional predictors involves transforming the functional data to wavelet domain and converting the data-fitting problem to a variable selection problem. Applying the LASSO procedure in this situation has been shown to be efficient and powerful. In this article, we explore two potential directions for improvements to this method: techniques for prescreening and methods for weighting the LASSO-type penalty. We consider several strategies for each of these directions which have never been investigated, either numerically or theoretically, in a functional linear regression context. We compare the finite-sample performance of the proposed methods through both simulations and real-data applications with both 1D signals and 2D image predictors. We also discuss asymptotic aspects. We show that applying these procedures can lead to improved estimation and prediction as well as better stability. Supplementary materials for this article are available online.

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Section: Consistent Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Wavelet-Based Weighted LASSO and Screening Approaches in Functional Linear Regression

Zhao¹,

Chen²,

Ogden³

2015

Journal of Computational and Graphical Statistics

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“…Not all sparse approaches rely on wavelet bases; see, for example, James et al. () and Lee and Park ().…”

Section: Linear Scalar‐on‐function Regressionmentioning

confidence: 99%

Methods for Scalar‐on‐Function Regression

Reiss

Goldsmith

Shang

et al. 2016

Int Statistical Rev

156

109

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Recent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images, etc. are considered as basic functional data units. A central problem in FDA is how to fit regression models with scalar responses and functional data points as predictors. We review some of the main approaches to this problem, categorizing the basic model types as linear, nonlinear and nonparametric. We discuss publicly available software packages, and illustrate some of the procedures by application to a functional magnetic resonance imaging dataset.

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“…scalar response and functional covariates) [2,4,8,9,12]. For the concurrent model, general solutions to the regularizations are studied in [5,11]; however, they are very computationally intensive due to the model complexity.…”

Section: Equivalence I: Fast Algorithm Of Regularized Functional Regrmentioning

confidence: 99%

Some equivalence relationships of regularized regressions

Zhang¹,

Thakar²,

Topham³

et al. 2018

Math. Appl.

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Abstract. Regularization is a powerful framework for solving ill-posed problem and preventing model overfitting in modern regression analysis. It is especially useful for high-dimensional or functional (infinite dimensional) regression models. In this paper, we construct two useful equivalence relationships for regularized regression:1. An equivalence between regularized functional regression and regularized multivariate regression. This equivalence provides a computationally efficient way to fit the concurrent functional regression model. 2. An equivalence of penalized multivariate regression under a group of scaling transformation. This equivalence can be used to solve weighted principal component regression efficiently.

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Sparse estimation in functional linear regression

Cited by 39 publications

References 22 publications

Wavelet-Based Weighted LASSO and Screening Approaches in Functional Linear Regression

Wavelet-Based Weighted LASSO and Screening Approaches in Functional Linear Regression

Methods for Scalar‐on‐Function Regression

Some equivalence relationships of regularized regressions

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