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Robust estimation for a general functional single index model via quantile regression. J Korean Stat Soc 2022. [DOI: 10.1007/s42952-022-00174-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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3
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Sparse semiparametric regression when predictors are mixture of functional and high-dimensional variables. TEST-SPAIN 2021. [DOI: 10.1007/s11749-020-00728-w] [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]
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4
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Wei Y, Chen D, Xiong S. Projection pursuit emulation for many-input computer experiments. COMMUN STAT-THEOR M 2020. [DOI: 10.1080/03610926.2020.1853772] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Yunfei Wei
- China Justice Big Data Institute CO., Ltd, Beijing, China
- NCMIS, KLSC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
| | | | - Shifeng Xiong
- NCMIS, KLSC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
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5
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Chaouch M, Bouchentouf AA, Traore A, Rabhi A. Single functional index quantile regression under general dependence structure. J Nonparametr Stat 2020. [DOI: 10.1080/10485252.2020.1797021] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Mohamed Chaouch
- Department of Mathematics, Statistics and Physics, Qatar University, Doha, Qatar
| | - Amina Angelika Bouchentouf
- Department of Mathematics, Laboratory of Mathematics, Djillali Liabes University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria
| | | | - Abbes Rabhi
- Department of Mathematics, Laboratory of Mathematics, Djillali Liabes University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria
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6
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Laa U, Cook D. Using tours to visually investigate properties of new projection pursuit indexes with application to problems in physics. Comput Stat 2020. [DOI: 10.1007/s00180-020-00954-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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7
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Affiliation(s)
- Pavel Čížek
- Department of Econometrics & Operations Research Tilburg University Tilburg The Netherlands
| | - Serhan Sadıkoğlu
- Department of Econometrics & Operations Research Tilburg University Tilburg The Netherlands
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8
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Dynamical multiple regression in function spaces, under kernel regressors, with ARH(1) errors. TEST-SPAIN 2019. [DOI: 10.1007/s11749-018-0614-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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9
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Zhu H, Zhang R, Yu Z, Lian H, Liu Y. Estimation and testing for partially functional linear errors-in-variables models. J MULTIVARIATE ANAL 2019. [DOI: 10.1016/j.jmva.2018.11.005] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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10
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Novo S, Aneiros G, Vieu P. Automatic and location-adaptive estimation in functional single-index regression. J Nonparametr Stat 2019. [DOI: 10.1080/10485252.2019.1567726] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Silvia Novo
- Departamento de Matemáticas, Universidade da Coruña, A Coruña, Spain
- Centro de Investigación de Tecnoloxías da Información e da Comunicación (CITIC), A Coruña, France
| | - Germán Aneiros
- Departamento de Matemáticas, Universidade da Coruña, A Coruña, Spain
- Centro de Investigación de Tecnoloxías da Información e da Comunicación (CITIC), A Coruña, France
- Instituto Tecnológico de Matemática Industrial (ITMATI), A Coruña, France
| | - Philippe Vieu
- Institut de Mathématiques, Université Paul Sabatier, Toulouse, France
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Chikr-Elmezouar Z, Almanjahie IM, Laksaci A, Rachdi M. FDA: strong consistency of the kNN local linear estimation of the functional conditional density and mode. J Nonparametr Stat 2018. [DOI: 10.1080/10485252.2018.1538450] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
| | - Ibrahim M. Almanjahie
- Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia
| | - Ali Laksaci
- Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia
| | - Mustapha Rachdi
- Laboratoire AGEIS EA 7407, TIMB Team, UFR SHS, Univ. Grenoble Alpes, Grenoble Cedex 09, France
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12
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Ling N, Vieu P. Nonparametric modelling for functional data: selected survey and tracks for future. STATISTICS-ABINGDON 2018. [DOI: 10.1080/02331888.2018.1487120] [Citation(s) in RCA: 46] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Nengxiang Ling
- School of Mathematics, Hefei University of Technology, Hefei, China
| | - Philippe Vieu
- Institut de Mathématiques, Université Paul Sabatier, Toulouse, France
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13
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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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15
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Predicting seasonal influenza transmission using functional regression models with temporal dependence. PLoS One 2018; 13:e0194250. [PMID: 29694350 PMCID: PMC5918942 DOI: 10.1371/journal.pone.0194250] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2017] [Accepted: 02/27/2018] [Indexed: 11/19/2022] Open
Abstract
This paper proposes a novel approach that uses meteorological information to predict the incidence of influenza in Galicia (Spain). It extends the Generalized Least Squares (GLS) methods in the multivariate framework to functional regression models with dependent errors. These kinds of models are useful when the recent history of the incidence of influenza are readily unavailable (for instance, by delays on the communication with health informants) and the prediction must be constructed by correcting the temporal dependence of the residuals and using more accessible variables. A simulation study shows that the GLS estimators render better estimations of the parameters associated with the regression model than they do with the classical models. They obtain extremely good results from the predictive point of view and are competitive with the classical time series approach for the incidence of influenza. An iterative version of the GLS estimator (called iGLS) was also proposed that can help to model complicated dependence structures. For constructing the model, the distance correlation measure R was employed to select relevant information to predict influenza rate mixing multivariate and functional variables. These kinds of models are extremely useful to health managers in allocating resources in advance to manage influenza epidemics.
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Yu P, Zhu Z, Zhang Z. Robust exponential squared loss-based estimation in semi-functional linear regression models. Comput Stat 2018. [DOI: 10.1007/s00180-018-0810-2] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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17
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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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Álvarez-Liébana J, Bosq D, Ruiz-Medina M. Asymptotic properties of a component-wise ARH(1) plug-in predictor. J MULTIVARIATE ANAL 2017. [DOI: 10.1016/j.jmva.2016.11.009] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Affiliation(s)
- G. Aneiros
- Departamento de Matemáticas, Universidad de A Coruña, A Coruña, Spain
| | - P. Vieu
- Institut de Mathématiques, Université Paul Sabatier, Toulouse, France
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Dabo-Niang S, Guillas S, Ternynck C. Efficiency in multivariate functional nonparametric models with autoregressive errors. J MULTIVARIATE ANAL 2016. [DOI: 10.1016/j.jmva.2016.01.007] [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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22
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Wang S, Huang M, Wu X, Yao W. Mixture of functional linear models and its application to CO 2-GDP functional data. Comput Stat Data Anal 2016. [DOI: 10.1016/j.csda.2015.11.008] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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23
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Montoya EL, Meiring W. An F-type test for detecting departure from monotonicity in a functional linear model. J Nonparametr Stat 2016. [DOI: 10.1080/10485252.2016.1163352] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Shang HL. A Bayesian approach for determining the optimal semi-metric and bandwidth in scalar-on-function quantile regression with unknown error density and dependent functional data. J MULTIVARIATE ANAL 2016. [DOI: 10.1016/j.jmva.2015.06.015] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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27
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Goia A, Vieu P. An introduction to recent advances in high/infinite dimensional statistics. J MULTIVARIATE ANAL 2016. [DOI: 10.1016/j.jmva.2015.12.001] [Citation(s) in RCA: 141] [Impact Index Per Article: 17.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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28
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Cleveland J, Wu W, Srivastava A. Norm-preserving constraint in the Fisher–Rao registration and its application in signal estimation. J Nonparametr Stat 2016. [DOI: 10.1080/10485252.2016.1163353] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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29
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Rejoinder on: Probability enhanced effective dimension reduction for classifying sparse functional data. TEST-SPAIN 2016. [DOI: 10.1007/s11749-015-0478-7] [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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30
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Petersen A, Müller HG. Fréchet integration and adaptive metric selection for interpretable covariances of multivariate functional data. Biometrika 2016. [DOI: 10.1093/biomet/asv054] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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31
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Abstract
A functional regression model with a scalar response and multiple functional predictors is proposed that accommodates two-way interactions in addition to their main effects. The proposed estimation procedure models the main effects using penalized regression splines, and the interaction effect by a tensor product basis. Extensions to generalized linear models and data observed on sparse grids or with measurement error are presented. A hypothesis testing procedure for the functional interaction effect is described. The proposed method can be easily implemented through existing software. Numerical studies show that fitting an additive model in the presence of interaction leads to both poor estimation performance and lost prediction power, while fitting an interaction model where there is in fact no interaction leads to negligible losses. The methodology is illustrated on the AneuRisk65 study data.
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Affiliation(s)
- JOSEPH USSET
- Kansas University Department of Biostatistics, Kansas City, KS, USA
| | | | - ARNAB MAITY
- North Carolina State Department of Statistics, Raleigh, NC, USA
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32
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Comments on: Probability enhanced effective dimension reduction for classifying sparse functional data. TEST-SPAIN 2016. [DOI: 10.1007/s11749-015-0471-1] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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33
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Ruiz-Medina M. Functional analysis of variance for Hilbert-valued multivariate fixed effect models. STATISTICS-ABINGDON 2015. [DOI: 10.1080/02331888.2015.1094069] [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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34
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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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35
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36
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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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Swihart BJ, Goldsmith J, Crainiceanu CM. Restricted Likelihood Ratio Tests for Functional Effects in the Functional Linear Model. Technometrics 2014. [DOI: 10.1080/00401706.2013.863163] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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41
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47
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Allam A, Mourid T. Covariance operator estimation of a functional autoregressive process with random coefficients. Stat Probab Lett 2014. [DOI: 10.1016/j.spl.2013.09.018] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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