1
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Park Y, Han K, Simpson DG. Testing Linear Operator Constraints in Functional Response Regression with Incomplete Response Functions. Electron J Stat 2023; 17:3143-3180. [PMID: 39105139 PMCID: PMC11299897 DOI: 10.1214/23-ejs2177] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/07/2024]
Abstract
Hypothesis testing procedures are developed to assess linear operator constraints in function-on-scalar regression when incomplete functional responses are observed. The approach enables statistical inferences about the shape and other aspects of the functional regression coefficients within a unified framework encompassing three incomplete sampling scenarios: (i) partially observed response functions as curve segments over random sub-intervals of the domain; (ii) discretely observed functional responses with additive measurement errors; and (iii) the composition of former two scenarios, where partially observed response segments are observed discretely with measurement error. The latter scenario has been little explored to date, although such structured data is increasingly common in applications. For statistical inference, deviations from the constraint space are measured via integratedL 2 -distance between the model estimates from the constrained and unconstrained model spaces. Large sample properties of the proposed test procedure are established, including the consistency, asymptotic distribution and local power of the test statistic. Finite sample power and level of the proposed test are investigated in a simulation study covering a variety of scenarios. The proposed methodologies are illustrated by applications to U.S. obesity prevalence data, analyzing the functional shape of its trends over time, and motion analysis in a study of automotive ergonomics.
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Affiliation(s)
- Yeonjoo Park
- Department of Management Science and Statistics, University of Texas at San Antonio, San Antonio, TX
| | - Kyunghee Han
- Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL
| | - Douglas G Simpson
- Department of Statistics, University of Illinois at Urbana-Champaign, Urbana-Champaign, IL
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2
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Wang Z, Magnotti J, Beauchamp MS, Li M. Functional group bridge for simultaneous regression and support estimation. Biometrics 2023; 79:1226-1238. [PMID: 35514244 PMCID: PMC9637240 DOI: 10.1111/biom.13684] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2020] [Accepted: 04/22/2022] [Indexed: 12/01/2022]
Abstract
This paper is motivated by studying differential brain activities to multiple experimental condition presentations in intracranial electroencephalography (iEEG) experiments. Contrasting effects of experimental conditions are often zero in most regions and nonzero in some local regions, yielding locally sparse functions. Such studies are essentially a function-on-scalar regression problem, with interest being focused not only on estimating nonparametric functions but also on recovering the function supports. We propose a weighted group bridge approach for simultaneous function estimation and support recovery in function-on-scalar mixed effect models, while accounting for heterogeneity present in functional data. We use B-splines to transform sparsity of functions to its sparse vector counterpart of increasing dimension, and propose a fast nonconvex optimization algorithm using nested alternative direction method of multipliers (ADMM) for estimation. Large sample properties are established. In particular, we show that the estimated coefficient functions are rate optimal in the minimax sense under the L2 norm and resemble a phase transition phenomenon. For support estimation, we derive a convergence rate under theL ∞ $L_{\infty }$ norm that leads to a selection consistency property under δ-sparsity, and obtain a result under strict sparsity using a simple sufficient regularity condition. An adjusted extended Bayesian information criterion is proposed for parameter tuning. The developed method is illustrated through simulations and an application to a novel iEEG data set to study multisensory integration.
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Affiliation(s)
- Zhengjia Wang
- Department of Statistics, Rice University, Houston, TX, USA
| | - John Magnotti
- Department of Neurosurgery, University of Pennsylvania Perelman School of Medicine, Philadelphia, PA, USA
| | - Michael S. Beauchamp
- Department of Neurosurgery, University of Pennsylvania Perelman School of Medicine, Philadelphia, PA, USA
| | - Meng Li
- Department of Statistics, Rice University, Houston, TX, USA
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3
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Collazos JAA, Dias R, Medeiros MC. Modeling the evolution of deaths from infectious diseases with functional data models: The case of COVID-19 in Brazil. Stat Med 2023; 42:993-1012. [PMID: 36631172 DOI: 10.1002/sim.9654] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2021] [Revised: 11/09/2022] [Accepted: 12/29/2022] [Indexed: 01/13/2023]
Abstract
In this paper, we apply statistical methods for functional data to explore the heterogeneity in the registered number of deaths of COVID-19, over time. The cumulative daily number of deaths in regions across Brazil is treated as continuous curves (functional data). The first stage of the analysis applies clustering methods for functional data to identify and describe potential heterogeneity in the curves and their functional derivatives. The estimated clusters are labeled with different "levels of alert" to identify cities in a possible critical situation. In the second stage of the analysis, we apply a functional quantile regression model for the death curves to explore the associations with functional rates of vaccination and stringency and also with several scalar geographical, socioeconomic and demographic covariates. The proposed model gave a better curve fit at different levels of the cumulative number of deaths when compared to a functional regression model based on ordinary least squares. Our results add to the understanding of the development of COVID-19 death counts.
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Affiliation(s)
- Julian A A Collazos
- Department of Mathematics, New Granada Military University, Bogotá, Colombia
| | - Ronaldo Dias
- Department of Statistics, State University of Campinas, Campinas, Brazil
| | - Marcelo C Medeiros
- Department of Economics, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil
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4
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Ghosal R, Maity A. Variable selection in nonlinear function-on-scalar regression. Biometrics 2023; 79:292-303. [PMID: 34528237 DOI: 10.1111/biom.13564] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2020] [Revised: 07/26/2021] [Accepted: 09/03/2021] [Indexed: 11/28/2022]
Abstract
We develop a new method for variable selection in a nonlinear additive function-on-scalar regression (FOSR) model. Existing methods for variable selection in FOSR have focused on the linear effects of scalar predictors, which can be a restrictive assumption in the presence of multiple continuously measured covariates. We propose a computationally efficient approach for variable selection in existing linear FOSR using functional principal component scores of the functional response and extend this framework to a nonlinear additive function-on-scalar model. The proposed method provides a unified and flexible framework for variable selection in FOSR, allowing nonlinear effects of the covariates. Numerical analysis using simulation study illustrates the advantages of the proposed method over existing variable selection methods in FOSR even when the underlying covariate effects are all linear. The proposed procedure is demonstrated on accelerometer data from the 2003-2004 cohorts of the National Health and Nutrition Examination Survey (NHANES) in understanding the association between diurnal patterns of physical activity and demographic, lifestyle, and health characteristics of the participants.
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Affiliation(s)
- Rahul Ghosal
- Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland
| | - Arnab Maity
- Department of Statistics, North Carolina State University, Raleigh, North Carolina
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5
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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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6
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Craig SJ, Kenney AM, Lin J, Paul IM, Birch LL, Savage JS, Marini ME, Chiaromonte F, Reimherr ML, Makova KD. Constructing a polygenic risk score for childhood obesity using functional data analysis. ECONOMETRICS AND STATISTICS 2023; 25:66-86. [PMID: 36620476 PMCID: PMC9813976 DOI: 10.1016/j.ecosta.2021.10.014] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Obesity is a highly heritable condition that affects increasing numbers of adults and, concerningly, of children. However, only a small fraction of its heritability has been attributed to specific genetic variants. These variants are traditionally ascertained from genome-wide association studies (GWAS), which utilize samples with tens or hundreds of thousands of individuals for whom a single summary measurement (e.g., BMI) is collected. An alternative approach is to focus on a smaller, more deeply characterized sample in conjunction with advanced statistical models that leverage longitudinal phenotypes. Novel functional data analysis (FDA) techniques are used to capitalize on longitudinal growth information from a cohort of children between birth and three years of age. In an ultra-high dimensional setting, hundreds of thousands of single nucleotide polymorphisms (SNPs) are screened, and selected SNPs are used to construct two polygenic risk scores (PRS) for childhood obesity using a weighting approach that incorporates the dynamic and joint nature of SNP effects. These scores are significantly higher in children with (vs. without) rapid infant weight gain-a predictor of obesity later in life. Using two independent cohorts, it is shown that the genetic variants identified in very young children are also informative in older children and in adults, consistent with early childhood obesity being predictive of obesity later in life. In contrast, PRSs based on SNPs identified by adult obesity GWAS are not predictive of weight gain in the cohort of young children. This provides an example of a successful application of FDA to GWAS. This application is complemented with simulations establishing that a deeply characterized sample can be just as, if not more, effective than a comparable study with a cross-sectional response. Overall, it is demonstrated that a deep, statistically sophisticated characterization of a longitudinal phenotype can provide increased statistical power to studies with relatively small sample sizes; and shows how FDA approaches can be used as an alternative to the traditional GWAS.
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Affiliation(s)
- Sarah J.C. Craig
- Department of Biology, Penn State University, University Park
- Center for Medical Genomics, Penn State University, University Park, PA
| | - Ana M. Kenney
- Department of Statistics, Penn State University, University Park, PA
| | - Junli Lin
- Department of Statistics, Penn State University, University Park, PA
| | - Ian M. Paul
- Center for Medical Genomics, Penn State University, University Park, PA
- Department of Pediatrics, Penn State College of Medicine, Hershey, PA
| | - Leann L. Birch
- Department of Foods and Nutrition, University of Georgia, Athens, GA
| | - Jennifer S. Savage
- Department of Nutritional Sciences, Penn State University, University Park, PA
- Center for Childhood Obesity Research, Penn State University, University Park, PA
| | - Michele E. Marini
- Center for Childhood Obesity Research, Penn State University, University Park, PA
| | - Francesca Chiaromonte
- Center for Medical Genomics, Penn State University, University Park, PA
- Department of Statistics, Penn State University, University Park, PA
- EMbeDS, Sant’Anna School of Advanced Studies, Piazza Martiri della Libertà, Pisa, Italy
| | - Matthew L. Reimherr
- Center for Medical Genomics, Penn State University, University Park, PA
- Department of Statistics, Penn State University, University Park, PA
| | - Kateryna D. Makova
- Department of Biology, Penn State University, University Park
- Center for Medical Genomics, Penn State University, University Park, PA
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7
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Meyer MJ, Morris JS, Gazes RP, Coull BA. Ordinal probit functional outcome regression with application to computer-use behavior in rhesus monkeys. Ann Appl Stat 2022; 16:537-550. [DOI: 10.1214/21-aoas1513] [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)
- Mark J. Meyer
- Department of Mathematics and Statistics, Georgetown University
| | - Jeffrey S. Morris
- Department of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine, University of Pennsylvania
| | - Regina Paxton Gazes
- Department of Psychology and Program in Animal Behavior, Bucknell University
| | - Brent A. Coull
- Department of Biostatistics, Harvard T.H. Chan School of Public Health
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8
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Li Y, Qiu Y, Xu Y. From multivariate to functional data analysis: fundamentals, recent developments, and emerging areas. J MULTIVARIATE ANAL 2022; 188:104806. [PMID: 39040141 PMCID: PMC11261241 DOI: 10.1016/j.jmva.2021.104806] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Functional data analysis (FDA), which is a branch of statistics on modeling infinite dimensional random vectors resided in functional spaces, has become a major research area for Journal of Multivariate Analysis. We review some fundamental concepts of FDA, their origins and connections from multivariate analysis, and some of its recent developments, including multi-level functional data analysis, high-dimensional functional regression, and dependent functional data analysis. We also discuss the impact of these new methodology developments on genetics, plant science, wearable device data analysis, image data analysis, and business analytics. Two real data examples are provided to motivate our discussions.
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Affiliation(s)
- Yehua Li
- University of California - Riverside, Riverside, CA 92521, USA
| | - Yumou Qiu
- Iowa State University, Ames, IA 50011, USA
| | - Yuhang Xu
- Bowling Green State University, Bowling Green, OH 43403, USA
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9
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Functional random forests for curve response. Sci Rep 2021; 11:24159. [PMID: 34921167 PMCID: PMC8683425 DOI: 10.1038/s41598-021-02265-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Accepted: 08/20/2021] [Indexed: 11/22/2022] Open
Abstract
The rapid advancement of functional data in various application fields has increased the demand for advanced statistical approaches that can incorporate complex structures and nonlinear associations. In this article, we propose a novel functional random forests (FunFor) approach to model the functional data response that is densely and regularly measured, as an extension of the landmark work of Breiman, who introduced traditional random forests for a univariate response. The FunFor approach is able to predict curve responses for new observations and selects important variables from a large set of scalar predictors. The FunFor approach inherits the efficiency of the traditional random forest approach in detecting complex relationships, including nonlinear and high-order interactions. Additionally, it is a non-parametric approach without the imposition of parametric and distributional assumptions. Eight simulation settings and one real-data analysis consistently demonstrate the excellent performance of the FunFor approach in various scenarios. In particular, FunFor successfully ranks the true predictors as the most important variables, while achieving the most robust variable sections and the smallest prediction errors when comparing it with three other relevant approaches. Although motivated by a biological leaf shape data analysis, the proposed FunFor approach has great potential to be widely applied in various fields due to its minimal requirement on tuning parameters and its distribution-free and model-free nature. An R package named 'FunFor', implementing the FunFor approach, is available at GitHub.
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10
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Mehrotra S, Maity A. Simultaneous variable selection, clustering, and smoothing in function‐on‐scalar regression. CAN J STAT 2021. [DOI: 10.1002/cjs.11668] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Suchit Mehrotra
- Department of Statistics North Carolina State University Raleigh NC U.S.A
| | - Arnab Maity
- Department of Statistics North Carolina State University Raleigh NC U.S.A
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11
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Cai X, Xue L, Cao J. Robust estimation and variable selection for function‐on‐scalar regression. CAN J STAT 2021. [DOI: 10.1002/cjs.11661] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Xiong Cai
- School of Statistics and Mathematics Nanjing Audit University Nanjing 211815 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 V5A1S6 BC Canada
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12
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Ghosal R, Maity A. Variable selection in nonparametric functional concurrent regression. CAN J STAT 2021. [DOI: 10.1002/cjs.11654] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Rahul Ghosal
- Department of Biostatistics Johns Hopkins University Baltimore MD U.S.A
| | - Arnab Maity
- Department of Statistics North Carolina State University Raleigh NC U.S.A
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13
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Moran KR, Dunson D, Wheeler MW, Herring AH. Bayesian joint modeling of chemical structure and dose response curves. Ann Appl Stat 2021; 15:1405-1430. [DOI: 10.1214/21-aoas1461] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
| | - David Dunson
- Department of Statistical Science, Duke University
| | - Matthew W. Wheeler
- Biostatistics and Computational Biology Branch, National Institute of Environmental Health Sciences
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14
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Adaptive function-on-scalar regression with a smoothing elastic net. J MULTIVARIATE ANAL 2021. [DOI: 10.1016/j.jmva.2021.104765] [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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15
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Aguilera-Morillo MC, Buño I, Lillo RE, Romo J. Variable selection with P-splines in functional linear regression: Application in graft-versus-host disease. Biom J 2020; 62:1670-1686. [PMID: 32520420 DOI: 10.1002/bimj.201900189] [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: 07/09/2019] [Revised: 11/29/2019] [Accepted: 01/07/2020] [Indexed: 11/12/2022]
Abstract
This paper focuses on the problems of estimation and variable selection in the functional linear regression model (FLM) with functional response and scalar covariates. To this end, two different types of regularization (L1 and L2 ) are considered in this paper. On the one hand, a sample approach for functional LASSO in terms of basis representation of the sample values of the response variable is proposed. On the other hand, we propose a penalized version of the FLM by introducing a P-spline penalty in the least squares fitting criterion. But our aim is to propose P-splines as a powerful tool simultaneously for variable selection and functional parameters estimation. In that sense, the importance of smoothing the response variable before fitting the model is also studied. In summary, penalized (L1 and L2 ) and nonpenalized regression are combined with a presmoothing of the response variable sample curves, based on regression splines or P-splines, providing a total of six approaches to be compared in two simulation schemes. Finally, the most competitive approach is applied to a real data set based on the graft-versus-host disease, which is one of the most frequent complications (30% -50%) in allogeneic hematopoietic stem-cell transplantation.
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Affiliation(s)
- M Carmen Aguilera-Morillo
- Department of Applied Statistics and Operations Research and Quality, Universitat Poltècnica de València, Valencia, Spain.,uc3m-Santander Big Data Institute, Madrid, Spain
| | - Ismael Buño
- Department of Hematology, Gregorio Marañón General University Hospital, Madrid, Spain.,Genomics Unit, Gregorio Marañón General University Hospital, Gregorio Marañón Health Research Institute (IiSGM), Madrid, Spain
| | - Rosa E Lillo
- uc3m-Santander Big Data Institute, Madrid, Spain.,Department of Statistics, Universidad Carlos III de Madrid, Madrid, Spain
| | - Juan Romo
- Department of Statistics, Universidad Carlos III de Madrid, Madrid, Spain
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16
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Ghosal R, Maity A, Clark T, Longo SB. Variable selection in functional linear concurrent regression. J R Stat Soc Ser C Appl Stat 2020. [DOI: 10.1111/rssc.12408] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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17
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Kong D, An B, Zhang J, Zhu H. L2RM: Low-rank Linear Regression Models for High-dimensional Matrix Responses. J Am Stat Assoc 2020; 115:403-424. [PMID: 33408427 PMCID: PMC7781207 DOI: 10.1080/01621459.2018.1555092] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2017] [Revised: 11/11/2018] [Accepted: 11/26/2018] [Indexed: 10/27/2022]
Abstract
The aim of this paper is to develop a low-rank linear regression model (L2RM) to correlate a high-dimensional response matrix with a high dimensional vector of covariates when coefficient matrices have low-rank structures. We propose a fast and efficient screening procedure based on the spectral norm of each coefficient matrix in order to deal with the case when the number of covariates is extremely large. We develop an efficient estimation procedure based on the trace norm regularization, which explicitly imposes the low rank structure of coefficient matrices. When both the dimension of response matrix and that of covariate vector diverge at the exponential order of the sample size, we investigate the sure independence screening property under some mild conditions. We also systematically investigate some theoretical properties of our estimation procedure including estimation consistency, rank consistency and non-asymptotic error bound under some mild conditions. We further establish a theoretical guarantee for the overall solution of our two-step screening and estimation procedure. We examine the finite-sample performance of our screening and estimation methods using simulations and a large-scale imaging genetic dataset collected by the Philadelphia Neurodevelopmental Cohort (PNC) study.
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Affiliation(s)
- Dehan Kong
- Department of Statistical Sciences, University of Toronto
| | - Baiguo An
- School of Statistics, Capital University of Economics and Business
| | - Jingwen Zhang
- Department of Biostatistics, University of North Carolina at Chapel Hill
| | - Hongtu Zhu
- Department of Biostatistics, University of North Carolina at Chapel Hill
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18
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Kowal DR, Bourgeois DC. Bayesian Function-on-Scalars Regression for High-Dimensional Data. J Comput Graph Stat 2020. [DOI: 10.1080/10618600.2019.1710837] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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19
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Conditional Analysis for Mixed Covariates, with Application to Feed Intake of Lactating Sows. JOURNAL OF PROBABILITY AND STATISTICS 2019. [DOI: 10.1155/2019/3743762] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We propose a novel modeling framework to study the effect of covariates of various types on the conditional distribution of the response. The methodology accommodates flexible model structure, allows for joint estimation of the quantiles at all levels, and provides a computationally efficient estimation algorithm. Extensive numerical investigation confirms good performance of the proposed method. The methodology is motivated by and applied to a lactating sow study, where the primary interest is to understand how the dynamic change of minute-by-minute temperature in the farrowing rooms within a day (functional covariate) is associated with low quantiles of feed intake of lactating sows, while accounting for other sow-specific information (vector covariate).
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20
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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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21
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Parodi A, Reimherr M. Simultaneous variable selection and smoothing for high-dimensional function-on-scalar regression. Electron J Stat 2018. [DOI: 10.1214/18-ejs1509] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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22
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Goldsmith J, Schwartz JE. Variable selection in the functional linear concurrent model. Stat Med 2017; 36:2237-2250. [PMID: 28211085 PMCID: PMC5457356 DOI: 10.1002/sim.7254] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2016] [Revised: 10/12/2016] [Accepted: 01/19/2017] [Indexed: 11/10/2022]
Abstract
We propose methods for variable selection in the context of modeling the association between a functional response and concurrently observed functional predictors. This data structure, and the need for such methods, is exemplified by our motivating example: a study in which blood pressure values are observed throughout the day, together with measurements of physical activity, location, posture, affect or mood, and other quantities that may influence blood pressure. We estimate the coefficients of the concurrent functional linear model using variational Bayes and jointly model residual correlation using functional principal components analysis. Latent binary indicators partition coefficient functions into included and excluded sets, incorporating variable selection into the estimation framework. The proposed methods are evaluated in simulations and real-data analyses, and are implemented in a publicly available R package with supporting interactive graphics for visualization. Copyright © 2017 John Wiley & Sons, Ltd.
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Affiliation(s)
- Jeff Goldsmith
- Department of Biostatistics, Columbia Mailman School of Public Health, Columbia University, New York, U.S.A
| | - Joseph E Schwartz
- Department of Medicine, Columbia University Medical Center, Columbia University, New York, U.S.A
- Department of Psychiatry and Behavioral Sciences, Stony Brook University, Stony Brook, U.S.A
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23
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Barber RF, Reimherr M, Schill T. The function-on-scalar LASSO with applications to longitudinal GWAS. Electron J Stat 2017. [DOI: 10.1214/17-ejs1260] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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