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Su Z, Li B, Cook D. Envelope model for function-on-function linear regression. J Comput Graph Stat 2023. [DOI: 10.1080/10618600.2022.2163652] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Affiliation(s)
- Zhihua Su
- Department of Statistics, University of Florida
| | - Bing Li
- Department of Statistics, Pennsylvania State University
| | - Dennis Cook
- School of Statistics, University of Minnesota
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2
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Adaptive smoothing spline estimator for the function-on-function linear regression model. Comput Stat 2022. [DOI: 10.1007/s00180-022-01223-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
AbstractIn 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 the true coefficient function over regions of large curvature and not to be undersmoothed over the remaining part of the domain. A novel evolutionary algorithm is developed ad hoc to obtain the optimization tuning parameters. Extensive Monte Carlo simulations have been carried out to compare the AdaSS estimator with competitors that have already appeared in the literature before. The results show that our proposal mostly outperforms the competitor in terms of estimation and prediction accuracy. Lastly, those advantages are illustrated also in two real-data benchmark examples. The AdaSS estimator is implemented in the package , openly available online on CRAN.
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3
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Lee KY, Li L. Functional sufficient dimension reduction through average Fréchet derivatives. Ann Stat 2022; 50:904-929. [PMID: 37041758 PMCID: PMC10085580 DOI: 10.1214/21-aos2131] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
Sufficient dimension reduction (SDR) embodies a family of methods that aim for reduction of dimensionality without loss of information in a regression setting. In this article, we propose a new method for nonparametric function-on-function SDR, where both the response and the predictor are a function. We first develop the notions of functional central mean subspace and functional central subspace, which form the population targets of our functional SDR. We then introduce an average Fréchet derivative estimator, which extends the gradient of the regression function to the operator level and enables us to develop estimators for our functional dimension reduction spaces. We show the resulting functional SDR estimators are unbiased and exhaustive, and more importantly, without imposing any distributional assumptions such as the linearity or the constant variance conditions that are commonly imposed by all existing functional SDR methods. We establish the uniform convergence of the estimators for the functional dimension reduction spaces, while allowing both the number of Karhunen-Loève expansions and the intrinsic dimension to diverge with the sample size. We demonstrate the efficacy of the proposed methods through both simulations and two real data examples.
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Affiliation(s)
- Kuang-Yao Lee
- Department of Statistical Science, Temple University
| | - Lexin Li
- Department of Biostatistics, University of California, Berkeley
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Abstract
In this article, we introduce a functional structural equation model for estimating directional relations from multivariate functional data. We decouple the estimation into two major steps: directional order determination and selection through sparse functional regression. We first propose a score function at the linear operator level, and show that its minimization can recover the true directional order when the relation between each function and its parental functions is nonlinear. We then develop a sparse functional additive regression, where both the response and the multivariate predictors are functions and the regression relation is additive and nonlinear. We also propose strategies to speed up the computation and scale up our method. In theory, we establish the consistencies of order determination, sparse functional additive regression, and directed acyclic graph estimation, while allowing both the dimension of the Karhunen-Loéve expansion coefficients and the number of random functions to diverge with the sample size. We illustrate the efficacy of our method through simulations, and an application to brain effective connectivity analysis.
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Affiliation(s)
| | - Lexin Li
- University of California Berkeley California USA
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5
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Fang Q, Guo S, Qiao X. Finite sample theory for high-dimensional functional/scalar time series with applications. Electron J Stat 2022. [DOI: 10.1214/21-ejs1960] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Qin Fang
- Department of Statistics, London School of Economics, London, WC2A 2AE, U.K
| | - Shaojun Guo
- Institute of Statistics and Big Data, Renmin University of China, Beijing, 100872, P.R. China
| | - Xinghao Qiao
- Department of Statistics, London School of Economics, London, WC2A 2AE, U.K
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6
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Fast implementation of partial least squares for function-on-function regression. J MULTIVARIATE ANAL 2021. [DOI: 10.1016/j.jmva.2021.104769] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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7
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Cai X, Xue L, Cao J. Robust penalized M‐estimation for function‐on‐function linear regression. Stat (Int Stat Inst) 2021. [DOI: 10.1002/sta4.390] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Xiong Cai
- College of Statistics and Data Science, Faculty of Science Beijing University of Technology Beijing 100124 China
| | - Liugen Xue
- College of Statistics and Data Science, Faculty of Science Beijing University of Technology Beijing 100124 China
| | - Jiguo Cao
- Department of Statistics and Actuarial Science Simon Fraser University Burnaby BC V5A1S6 Canada
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8
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Luo R, Qi X. Restricted function-on-function linear regression model. Biometrics 2021; 78:1031-1044. [PMID: 33792034 DOI: 10.1111/biom.13463] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2020] [Revised: 03/09/2021] [Accepted: 03/15/2021] [Indexed: 11/29/2022]
Abstract
The usual function-on-function linear regression model depicts the association between functional variables in the whole rectangular region and the value of response curve at any point is influenced by the entire trajectory of the predictor curve. But in addition to this, there are cases where the value of the response curve at a point is only influenced by the value of the predictor curve in a subregion, such as the historical relationship and the short-term association. We will consider the restricted function-on-function regression model, where the value of response curve at any point is influenced by a subtrajectory of the predictor. We have two major purposes. First, we propose a novel estimation procedure that is more accurate and computational efficient for the restricted function-on-function model with a given subregion. Second, as the subregion is seldom specified in practice, we propose a subregion selection procedure that can lead to models with better interpretation and predictive performance. Algorithms are developed for both model estimation and subregion selection.
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Affiliation(s)
- Ruiyan Luo
- Department of Population Health Sciences, School of Public Health, Georgia State University, Atlanta, Georgia, USA
| | - Xin Qi
- Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia, USA
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9
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Xu W, Ding H, Zhang R, Liang H. Estimation and inference in partially functional linear regression with multiple functional covariates. J Stat Plan Inference 2020. [DOI: 10.1016/j.jspi.2020.02.007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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10
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Luo R, Qi X. Functional Regression for Densely Observed Data With Novel Regularization. J Comput Graph Stat 2020. [DOI: 10.1080/10618600.2020.1807994] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Ruiyan Luo
- Department of Population Health Sciences, School of Public Health, Georgia State University, Atlanta, GA
| | - Xin Qi
- Department of Mathematics and Statistics, Georgia State University, Atlanta, GA
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11
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Abstract
Covariance estimation is essential yet underdeveloped for analyzing multivariate functional data. We propose a fast covariance estimation method for multivariate sparse functional data using bivariate penalized splines. The tensor-product B-spline formulation of the proposed method enables a simple spectral decomposition of the associated covariance operator and explicit expressions of the resulting eigenfunctions as linear combinations of B-spline bases, thereby dramatically facilitating subsequent principal component analysis. We derive a fast algorithm for selecting the smoothing parameters in covariance smoothing using leave-one-subject-out cross-validation. The method is evaluated with extensive numerical studies and applied to an Alzheimer's disease study with multiple longitudinal outcomes.
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Affiliation(s)
- Cai Li
- Department of Statistics, North Carolina State Univerisy, NC, USA
| | - Luo Xiao
- Department of Statistics, North Carolina State Univerisy, NC, USA
| | - Sheng Luo
- Department of Biostatistics and Bioinformatics, Duke Universitye, NC, USA
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12
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Cao G, Wang S, Wang L. Estimation and inference for functional linear regression models with partially varying regression coefficients. Stat (Int Stat Inst) 2020. [DOI: 10.1002/sta4.286] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Guanqun Cao
- Department of Mathematics and Statistics Auburn University Auburn 36849 AL USA
| | - Shuoyang Wang
- Department of Mathematics and Statistics Auburn University Auburn 36849 AL USA
| | - Lily Wang
- Department of Statistics Iowa State University Ames 50011 IA USA
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13
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Centofanti F, Lepore A, Menafoglio A, Palumbo B, Vantini S. Functional Regression Control Chart. Technometrics 2020. [DOI: 10.1080/00401706.2020.1753581] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Fabio Centofanti
- Department of Industrial Engineering, University of Naples Federico II, Naples, Italy
| | - Antonio Lepore
- Department of Industrial Engineering, University of Naples Federico II, Naples, Italy
| | - Alessandra Menafoglio
- MOX – Modelling and Scientific Computing, Department of Mathematics, Politecnico di Milano, Milan, Italy
| | - Biagio Palumbo
- Department of Industrial Engineering, University of Naples Federico II, Naples, Italy
| | - Simone Vantini
- MOX – Modelling and Scientific Computing, Department of Mathematics, Politecnico di Milano, Milan, Italy
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14
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Zhang X, Zhong Q, Wang JL. A new approach to varying-coefficient additive models with longitudinal covariates. Comput Stat Data Anal 2020. [DOI: 10.1016/j.csda.2020.106912] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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16
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Gahrooei MR, Yan H, Paynabar K, Shi J. Multiple Tensor-on-Tensor Regression: An Approach for Modeling Processes With Heterogeneous Sources of Data. Technometrics 2020. [DOI: 10.1080/00401706.2019.1708463] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Mostafa Reisi Gahrooei
- Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL
| | - Hao Yan
- School of Computing, Informatics, & Decision Systems Engineering, Arizona State University, Tempe, AZ
| | - Kamran Paynabar
- H. Milton Stewart School of Industrial & Systems Engineering, Georgia Institute of Technology, Atlanta, GA
| | - Jianjun Shi
- H. Milton Stewart School of Industrial & Systems Engineering, Georgia Institute of Technology, Atlanta, GA
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Mostafaiy B, Faridrohani MR, Chenouri S. Optimal estimation in functional linear regression for sparse noise‐contaminated data. CAN J STAT 2019. [DOI: 10.1002/cjs.11511] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Affiliation(s)
- Behdad Mostafaiy
- Department of Statistics, University of Mohaghegh Ardabili, Daneshgah Street, Ardabil 56199‐11367, Iran
| | | | - Shojaeddin Chenouri
- Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
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Affiliation(s)
- Ruiyan Luo
- Division of Epidemiology and Biostatistics, School of Public Health, Georgia State University, Atlanta, GA
| | - Xin Qi
- Department of Mathematics and Statistics, Georgia State University, Atlanta, GA
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