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Zhang C, Lin H, Liu L, Liu J, Li Y. Functional data analysis with covariate-dependent mean and covariance structures. Biometrics 2023; 79:2232-2245. [PMID: 36065564 DOI: 10.1111/biom.13744] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2021] [Accepted: 08/11/2022] [Indexed: 11/27/2022]
Abstract
Functional data analysis has emerged as a powerful tool in response to the ever-increasing resources and efforts devoted to collecting information about response curves or anything that varies over a continuum. However, limited progress has been made with regard to linking the covariance structures of response curves to external covariates, as most functional models assume a common covariance structure. We propose a new functional regression model with covariate-dependent mean and covariance structures. Particularly, by allowing variances of random scores to be covariate-dependent, we identify eigenfunctions for each individual from the set of eigenfunctions that govern the variation patterns across all individuals, resulting in high interpretability and prediction power. We further propose a new penalized quasi-likelihood procedure that combines regularization and B-spline smoothing for model selection and estimation and establish the convergence rate and asymptotic normality of the proposed estimators. The utility of the developed method is demonstrated via simulations, as well as an analysis of the Avon Longitudinal Study of Parents and Children concerning parental effects on the growth curves of their offspring, which yields biologically interesting results.
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Affiliation(s)
- Chenlin Zhang
- Center of Statistical Research and School of Statistics, Southwestern University of Finance and Economics, Chengdu, China
| | - Huazhen Lin
- Center of Statistical Research and School of Statistics, Southwestern University of Finance and Economics, Chengdu, China
| | - Li Liu
- School of Mathematics and Statistics, Wuhan University, Wuhan, China
| | - Jin Liu
- Centre for Quantitative Medicine, Program in Health Services & Systems Research, Duke-NUS Medical School, Singapore
| | - Yi Li
- Department of Biostatistics, University of Michigan, Ann Arbor, Michigan, USA
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2
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Shape-constrained estimation in functional regression with Bernstein polynomials. Comput Stat Data Anal 2023. [DOI: 10.1016/j.csda.2022.107614] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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3
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Rao AR, Reimherr M. Non-linear Functional Modeling using Neural Networks. J Comput Graph Stat 2023. [DOI: 10.1080/10618600.2023.2165498] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
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4
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Lundborg AR, Shah RD, Peters J. Conditional independence testing in Hilbert spaces with applications to functional data analysis. J R Stat Soc Series B Stat Methodol 2022. [DOI: 10.1111/rssb.12544] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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5
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Dubey P, Chen Y, Gajardo Á, Bhattacharjee S, Carroll C, Zhou Y, Chen H, Müller HG. Learning delay dynamics for multivariate stochastic processes, with application to the prediction of the growth rate of COVID-19 cases in the United States. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2022; 514:125677. [PMID: 34642503 PMCID: PMC8494512 DOI: 10.1016/j.jmaa.2021.125677] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/11/2020] [Indexed: 06/13/2023]
Abstract
Delay differential equations form the underpinning of many complex dynamical systems. The forward problem of solving random differential equations with delay has received increasing attention in recent years. Motivated by the challenge to predict the COVID-19 caseload trajectories for individual states in the U.S., we target here the inverse problem. Given a sample of observed random trajectories obeying an unknown random differential equation model with delay, we use a functional data analysis framework to learn the model parameters that govern the underlying dynamics from the data. We show the existence and uniqueness of the analytical solutions of the population delay random differential equation model when one has discrete time delays in the functional concurrent regression model and also for a second scenario where one has a delay continuum or distributed delay. The latter involves a functional linear regression model with history index. The derivative of the process of interest is modeled using the process itself as predictor and also other functional predictors with predictor-specific delayed impacts. This dynamics learning approach is shown to be well suited to model the growth rate of COVID-19 for the states that are part of the U.S., by pooling information from the individual states, using the case process and concurrently observed economic and mobility data as predictors.
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Affiliation(s)
- Paromita Dubey
- Department of Statistics, Stanford University, United States of America
| | - Yaqing Chen
- Department of Statistics, University of California, Davis, United States of America
| | - Álvaro Gajardo
- Department of Statistics, University of California, Davis, United States of America
| | | | - Cody Carroll
- Department of Statistics, University of California, Davis, United States of America
| | - Yidong Zhou
- Department of Statistics, University of California, Davis, United States of America
| | - Han Chen
- Department of Statistics, University of California, Davis, United States of America
| | - Hans-Georg Müller
- Department of Statistics, University of California, Davis, United States of America
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6
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Xiao P, Wang G. Partial functional linear regression with autoregressive errors. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2020.1818097] [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)
- Piaoxuan Xiao
- College of Economics, Jinan University, Guangzhou, China
| | - Guochang Wang
- College of Economics, Jinan University, Guangzhou, China
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7
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Feng S, Zhang X, Liang H, Pei L. Model selection for functional linear regression with hierarchical structure. BRAZ J PROBAB STAT 2022. [DOI: 10.1214/21-bjps525] [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)
- Sanying Feng
- School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
| | - Xinyu Zhang
- School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
| | - Hui Liang
- School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
| | - Lifang Pei
- School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
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Xu W, Lin H, Zhang R, Liang H. Two-sample functional linear models with functional responses. J Stat Plan Inference 2022. [DOI: 10.1016/j.jspi.2021.10.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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9
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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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10
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Zhao F, Lin N, Hu W, Zhang B. A faster U-statistic for testing independence in the functional linear models. J Stat Plan Inference 2022. [DOI: 10.1016/j.jspi.2021.08.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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11
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Jiang J, Lin H, Peng H, Fan G, Li Y. Cluster analysis with regression of non‐Gaussian functional data on covariates. CAN J STAT 2021. [DOI: 10.1002/cjs.11680] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Affiliation(s)
- Jiakun Jiang
- Center for Statistics and Data Science Beijing Normal University at Zhuhai Zhuhai China
- Center of Statistical Research and School of Statistics Southwestern University of Finance and Economics Chengdu Sichuan China
| | - Huazhen Lin
- Center of Statistical Research and School of Statistics Southwestern University of Finance and Economics Chengdu Sichuan China
| | - Heng Peng
- Department of Mathematics Hong Kong Baptist University Hong Kong China
| | - Gang‐Zhi Fan
- School of Management Guangzhou University Guangzhou China
| | - Yi Li
- Department of Biostatistics University of Michigan Ann Arbor MI48109 U.S.A
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12
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Bagging-Enhanced Sampling Schedule for Functional Quadratic Regression. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2021. [DOI: 10.1007/s42519-021-00223-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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13
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Zhang T, Huo H, Wan Y. Functional polynomial multiple-index model. COMMUN STAT-SIMUL C 2021. [DOI: 10.1080/03610918.2019.1635156] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Tao Zhang
- School of Science, Guangxi University of Science and Technology, Liuzhou, China
| | - Haifeng Huo
- School of Science, Guangxi University of Science and Technology, Liuzhou, China
| | - Yanling Wan
- School of Social Science, Guangxi University of Science and Technology, Liuzhou, China
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14
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Shi H, Ma D, Faisal Beg M, Cao J. A functional proportional hazard cure rate model for interval-censored data. Stat Methods Med Res 2021; 31:154-168. [PMID: 34806480 DOI: 10.1177/09622802211052972] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Existing survival models involving functional covariates typically rely on the Cox proportional hazards structure and the assumption of right censorship. Motivated by the aim of predicting the time of conversion to Alzheimer's disease from sparse biomarker trajectories in patients with mild cognitive impairment, we propose a functional mixture cure rate model with both functional and scalar covariates for interval censoring and sparsely sampled functional data. To estimate the nonparametric coefficient function that depicts the effect of the shape of the trajectories on the survival outcome and cure probability, we utilize the functional principal component analysis to extract the functional features from the sparsely and irregularly sampled trajectories. To obtain parameter estimates from the mixture cure rate model with interval censoring, we apply the expectation-maximization algorithm based on Poisson data augmentation. The estimation accuracy of our method is assessed via a simulation study and we apply our model on Alzheimer's disease Neuroimaging Initiative data set.
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Affiliation(s)
- Haolun Shi
- Department of Statistics and Actuarial Science, 1763Simon Fraser University, Burnaby, BC, Canada
| | - Da Ma
- School of Engineering, 1763Simon Fraser University, Burnaby, BC, Canada
| | - Mirza Faisal Beg
- School of Engineering, 1763Simon Fraser University, Burnaby, BC, Canada
| | - Jiguo Cao
- Department of Statistics and Actuarial Science, 1763Simon Fraser University, Burnaby, BC, Canada
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15
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16
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Lai T, Zhang Z, Wang Y. A kernel-based measure for conditional mean dependence. Comput Stat Data Anal 2021. [DOI: 10.1016/j.csda.2021.107246] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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17
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Affossogbe MMR, Martial Nkiet G, Ogouyandjou C. Smoothed average variance estimation for dimension reduction with functional data. COMMUN STAT-THEOR M 2021. [DOI: 10.1080/03610926.2021.1931330] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
| | - Guy Martial Nkiet
- Université des Sciences et Techniques de Masuku, Département de Mathématiques et Informatique, Franceville, Gabon
| | - Carlos Ogouyandjou
- Institut de Mathématiques et de Sciences Physiques, Département de Mathématiques, Porto Novo, Bénin
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18
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Feng S, Zhang M, Tong T. Variable selection for functional linear models with strong heredity constraint. ANN I STAT MATH 2021. [DOI: 10.1007/s10463-021-00798-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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19
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20
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Mojirsheibani M, Nguyen MN. On statistical classification with incomplete covariates via filtering. J STAT COMPUT SIM 2020. [DOI: 10.1080/00949655.2020.1856379] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Majid Mojirsheibani
- Department of Mathematics, California State University Northridge, Los Angeles, CA, USA
| | - My-Nhi Nguyen
- Department of Preventive Medicine, University of Southern California, Los Angeles, CA, USA
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21
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Patilea V, Sánchez-Sellero C. Testing for lack-of-fit in functional regression models against general alternatives. J Stat Plan Inference 2020. [DOI: 10.1016/j.jspi.2020.04.002] [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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22
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23
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Abstract
Summary
We propose a new method for functional nonparametric regression with a predictor that resides on a finite-dimensional manifold, but is observable only in an infinite-dimensional space. Contamination of the predictor due to discrete or noisy measurements is also accounted for. By using functional local linear manifold smoothing, the proposed estimator enjoys a polynomial rate of convergence that adapts to the intrinsic manifold dimension and the contamination level. This is in contrast to the logarithmic convergence rate in the literature of functional nonparametric regression. We also observe a phase transition phenomenon related to the interplay between the manifold dimension and the contamination level. We demonstrate via simulated and real data examples that the proposed method has favourable numerical performance relative to existing commonly used methods.
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Affiliation(s)
- Zhenhua Lin
- Department of Statistics and Applied Probability, National University of Singapore, 117546 Singapore
| | - Fang Yao
- Department of Probability and Statistics, School of Mathematical Sciences, Center for Statistical Science, Peking University, Beijing 100871, China
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24
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Shi G, Xie T, Zhang Z. Statistical inference for the functional quadratic quantile regression model. METRIKA 2020. [DOI: 10.1007/s00184-020-00763-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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25
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26
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Huang T, Saporta G, Wang H, Wang S. A robust spatial autoregressive scalar-on-function regression with t-distribution. ADV DATA ANAL CLASSI 2020. [DOI: 10.1007/s11634-020-00384-w] [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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27
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28
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Gaussian process methods for nonparametric functional regression with mixed predictors. Comput Stat Data Anal 2019. [DOI: 10.1016/j.csda.2018.07.009] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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29
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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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30
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31
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Tekbudak MY, Alfaro-Córdoba M, Maity A, Staicu AM. A comparison of testing methods in scalar-on-function regression. ASTA ADVANCES IN STATISTICAL ANALYSIS 2018. [DOI: 10.1007/s10182-018-00337-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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32
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Duda P, Jaworski M, Rutkowski L. Knowledge discovery in data streams with the orthogonal series-based generalized regression neural networks. Inf Sci (N Y) 2018. [DOI: 10.1016/j.ins.2017.07.013] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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33
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Han K, Müller HG, Park BU. Smooth backfitting for additive modeling with small errors-in-variables, with an application to additive functional regression for multiple predictor functions. BERNOULLI 2018. [DOI: 10.3150/16-bej898] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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34
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Zhang T, Dai P, Zhang Q. Joint detection for functional polynomial regression with autoregressive errors. COMMUN STAT-THEOR M 2017. [DOI: 10.1080/03610926.2015.1096384] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Tao Zhang
- School of Science, Guangxi University of Science and Technology, Liuzhou, China
- Guangxi Colleges and Universities Key Laboratory of Mathematics and Statistical Model, Guilin, China
| | - Pengjie Dai
- School of Business, Renmin University of China, Beijing, China
| | - Qingzhao Zhang
- School of Economics and the Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, China
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35
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Reiss PT, Goldsmith J, Shang HL, Ogden RT. Methods for scalar-on-function regression. Int Stat Rev 2017; 85:228-249. [PMID: 28919663 PMCID: PMC5598560 DOI: 10.1111/insr.12163] [Citation(s) in RCA: 72] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2015] [Accepted: 12/28/2015] [Indexed: 01/16/2023]
Abstract
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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Affiliation(s)
- Philip T. Reiss
- Department of Child and Adolescent Psychiatry and Department of Population Health, New York University School of Medicine
- Department of Statistics, University of Haifa
| | - Jeff Goldsmith
- Department of Biostatistics, Columbia University Mailman School of Public Health
| | - Han Lin Shang
- Research School of Finance, Actuarial Studies and Statistics, Australian National University
| | - R. Todd Ogden
- Department of Biostatistics, Columbia University Mailman School of Public Health
- New York State Psychiatric Institute
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36
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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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37
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Lakraj GP, Ruymgaart F. Some asymptotic theory for Silverman’s smoothed functional principal components in an abstract Hilbert space. J MULTIVARIATE ANAL 2017. [DOI: 10.1016/j.jmva.2016.12.004] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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38
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Veisi F, Zazouli MA, Ebrahimzadeh MA, Charati JY, Dezfoli AS. Photocatalytic degradation of furfural in aqueous solution by N-doped titanium dioxide nanoparticles. ENVIRONMENTAL SCIENCE AND POLLUTION RESEARCH INTERNATIONAL 2016; 23:21846-21860. [PMID: 27525742 DOI: 10.1007/s11356-016-7199-7] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2016] [Accepted: 07/06/2016] [Indexed: 06/06/2023]
Abstract
The photocatalytic degradation of furfural in aqueous solution was investigated using N-doped titanium dioxide nanoparticles under sunlight and ultraviolet radiation (N-TiO2/Sun and N-TiO2/UV) in a lab-scale batch photoreactor. The N-TiO2 nanoparticles prepared using a sol-gel method were characterized using XRD, X-ray photoelectron spectroscopy (XPS), and SEM analyses. Using HPLC to monitor the furfural concentration, the effect of catalyst dosage, contact time, initial solution pH, initial furfural concentration, and sunlight or ultraviolet radiation on the degradation efficiency was studied. The efficiency of furfural removal was found to increase with increased reaction time, nanoparticle loading, and pH for both processes, whereas the efficiency decreased with increased furfural concentration. The maximum removal efficiencies for the N-TiO2/UV and N-TiO2/Sun processes were 97 and 78 %, respectively, whereas the mean removal efficiencies were 80.71 ± 2.08 % and 62.85 ± 2.41 %, respectively. In general, the degradation and elimination rate of furfural using the N-TiO2/UV process was higher than that using the N-TiO2/Sun process.
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Affiliation(s)
- Farzaneh Veisi
- Health Sciences Research Center, Student Research Committee, Mazandaran University of Medical Sciences, Sari, Iran
| | - Mohammad Ali Zazouli
- Department of Environmental Health Engineering, Faculty of Heath, Health Sciences Research Center, Mazandaran University of Medical Sciences, Sari, Iran.
| | - Mohammad Ali Ebrahimzadeh
- Department of Pharmaceutical Chemistry, Faculty of Pharmacy, Mazandaran University of Medical Sciences, Sari, Iran
| | - Jamshid Yazdani Charati
- Department of Biostatics, Faculty of Health, Health Sciences Research Center, Mazandaran University of Medical Sciences, Sari, Iran
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39
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Zhang T, Zhang Q, Li N. Least absolute relative error estimation for functional quadratic multiplicative model. COMMUN STAT-THEOR M 2016. [DOI: 10.1080/03610926.2014.950748] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Tao Zhang
- School of Science, Guangxi University of Science and Technology, Liuzhou, China
| | - Qingzhao Zhang
- School of Economics and the Wang Yanan Institute for Studies in Economics, Xiamen University, China
| | - Naixiong Li
- School of Science, Guangxi University of Science and Technology, Liuzhou, China
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40
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Abstract
This article addresses estimation in regression models for longitudinally-collected functional covariates (time-varying predictor curves) with a longitudinal scaler outcome. The framework consists of estimating a time-varying coefficient function that is modeled as a linear combination of time-invariant functions with time-varying coefficients. The model uses extrinsic information to inform the structure of the penalty, while the estimation procedure exploits the equivalence between penalized least squares estimation and a linear mixed model representation. The process is empirically evaluated with several simulations and it is applied to analyze the neurocognitive impairment of HIV patients and its association with longitudinally-collected magnetic resonance spectroscopy (MRS) curves.
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Affiliation(s)
- Madan G Kundu
- Novartis Pharmaceuticals Corporation (Oncology) East Hanover, NJ, USA
| | - Jaroslaw Harezlak
- Department of Biostatistics, Indiana University RM Fairbanks School of Public Health, IN, USA
| | - Timothy W Randolph
- Biostatistics and Biomathematics Program, Fred Hutchinson Cancer Research Center, WA, USA
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41
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Khademnoe O, Hosseini-Nasab SME. On properties of percentile bootstrap confidence intervals for prediction in functional linear regression. J Stat Plan Inference 2016. [DOI: 10.1016/j.jspi.2015.10.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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42
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Kong D, Xue K, Yao F, Zhang HH. Partially functional linear regression in high dimensions. Biometrika 2016. [DOI: 10.1093/biomet/asv062] [Citation(s) in RCA: 82] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
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43
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Luo R, Qi X, Wang Y. Functional wavelet regression for linear function-on-function models. Electron J Stat 2016. [DOI: 10.1214/16-ejs1204] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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44
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Scheipl F, Greven S. Identifiability in penalized function-on-function regression models. Electron J Stat 2016. [DOI: 10.1214/16-ejs1123] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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45
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Chen K, Zhang X, Petersen A, Müller HG. Quantifying Infinite-Dimensional Data: Functional Data Analysis in Action. STATISTICS IN BIOSCIENCES 2015. [DOI: 10.1007/s12561-015-9137-5] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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46
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Wang G, Zhou Y, Feng XN, Zhang B. The hybrid method of FSIR and FSAVE for functional effective dimension reduction. Comput Stat Data Anal 2015. [DOI: 10.1016/j.csda.2015.05.011] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Asymptotic results of a nonparametric conditional cumulative distribution estimator in the single functional index modeling for time series data with applications. METRIKA 2015. [DOI: 10.1007/s00184-015-0564-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Febrero-Bande M, Galeano P, González-Manteiga W. Functional Principal Component Regression and Functional Partial Least-squares Regression: An Overview and a Comparative Study. Int Stat Rev 2015. [DOI: 10.1111/insr.12116] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Affiliation(s)
| | - Xiang‐Nan Feng
- Department of Statistics The Chinese University of Hong Kong
| | - Min Chen
- Academy of Mathematics System Science Chinese Academy of Sciences
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