1
|
Wang Z, Bai Y, Härdle WK, Tian M. Smoothed quantile regression for partially functional linear models in high dimensions. Biom J 2023; 65:e2200060. [PMID: 37147793 DOI: 10.1002/bimj.202200060] [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: 02/26/2022] [Revised: 11/21/2022] [Accepted: 12/11/2022] [Indexed: 05/07/2023]
Abstract
Practitioners of current data analysis are regularly confronted with the situation where the heavy-tailed skewed response is related to both multiple functional predictors and high-dimensional scalar covariates. We propose a new class of partially functional penalized convolution-type smoothed quantile regression to characterize the conditional quantile level between a scalar response and predictors of both functional and scalar types. The new approach overcomes the lack of smoothness and severe convexity of the standard quantile empirical loss, considerably improving the computing efficiency of partially functional quantile regression. We investigate a folded concave penalized estimator for simultaneous variable selection and estimation by the modified local adaptive majorize-minimization (LAMM) algorithm. The functional predictors can be dense or sparse and are approximated by the principal component basis. Under mild conditions, the consistency and oracle properties of the resulting estimators are established. Simulation studies demonstrate a competitive performance against the partially functional standard penalized quantile regression. A real application using Alzheimer's Disease Neuroimaging Initiative data is utilized to illustrate the practicality of the proposed model.
Collapse
Affiliation(s)
- Zhihao Wang
- Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing, P. R. China
- School of Statistics and Data Science, Xinjiang University of Finance and Economics, Urumqi, P. R. China
| | - Yongxin Bai
- School of Science, Beijing Information Science and Technology University, Beijing, P. R. China
| | - Wolfgang K Härdle
- School of Business and Economics, Humboldt-Universität Zu Berlin, Berlin, Germany
- Department of Information Management and Finance, National Yang Ming Chiao Tung University (NYCU), Hsinchu City, Taiwan
| | - Maozai Tian
- Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing, P. R. China
- School of Statistics and Data Science, Xinjiang University of Finance and Economics, Urumqi, P. R. China
| |
Collapse
|
2
|
Yan X, Yu J, Ding W, Wang H, Zhao P. A novel two-way functional linear model with applications in human mortality data analysis. J Appl Stat 2023; 51:2025-2038. [PMID: 39071246 PMCID: PMC11271083 DOI: 10.1080/02664763.2023.2253379] [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: 03/01/2023] [Accepted: 08/15/2023] [Indexed: 07/30/2024]
Abstract
Recently, two-way or longitudinal functional data analysis has attracted much attention in many fields. However, little is known on how to appropriately characterize the association between two-way functional predictor and scalar response. Motivated by a mortality study, in this paper, we propose a novel two-way functional linear model, where the response is a scalar and functional predictor is two-way trajectory. The model is intuitive, interpretable and naturally captures relationship between each way of two-way functional predictor and scalar-type response. Further, we develop a new estimation method to estimate the regression functions in the framework of weak separability. The main technical tools for the construction of the regression functions are product functional principal component analysis and iterative least square procedure. The solid performance of our method is demonstrated in extensive simulation studies. We also analyze the mortality dataset to illustrate the usefulness of the proposed procedure.
Collapse
Affiliation(s)
- Xingyu Yan
- School of Mathematics and Statistics and RIMS, Jiangsu Provincial Key Laboratory of Educational Big Data Science and Engineering, Jiangsu Normal University, Xuzhou, Jiangsu, People's Republic of China
| | - Jiaqian Yu
- School of Mathematics and Statistics and RIMS, Jiangsu Provincial Key Laboratory of Educational Big Data Science and Engineering, Jiangsu Normal University, Xuzhou, Jiangsu, People's Republic of China
| | - Weiyong Ding
- School of Mathematics and Statistics and RIMS, Jiangsu Provincial Key Laboratory of Educational Big Data Science and Engineering, Jiangsu Normal University, Xuzhou, Jiangsu, People's Republic of China
| | - Hao Wang
- School of Mathematics and Statistics, Anhui Normal University, Wuhu, People's Republic of China
| | - Peng Zhao
- School of Mathematics and Statistics and RIMS, Jiangsu Provincial Key Laboratory of Educational Big Data Science and Engineering, Jiangsu Normal University, Xuzhou, Jiangsu, People's Republic of China
| |
Collapse
|
3
|
Wang W, Sun Y, Wang HJ. Latent group detection in functional partially linear regression models. Biometrics 2023; 79:280-291. [PMID: 34482542 DOI: 10.1111/biom.13557] [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] [Received: 06/27/2020] [Revised: 08/06/2021] [Accepted: 08/19/2021] [Indexed: 11/28/2022]
Abstract
In this paper, we propose a functional partially linear regression model with latent group structures to accommodate the heterogeneous relationship between a scalar response and functional covariates. The proposed model is motivated by a salinity tolerance study of barley families, whose main objective is to detect salinity tolerant barley plants. Our model is flexible, allowing for heterogeneous functional coefficients while being efficient by pooling information within a group for estimation. We develop an algorithm in the spirit of the K-means clustering to identify latent groups of the subjects under study. We establish the consistency of the proposed estimator, derive the convergence rate and the asymptotic distribution, and develop inference procedures. We show by simulation studies that the proposed method has higher accuracy for recovering latent groups and for estimating the functional coefficients than existing methods. The analysis of the barley data shows that the proposed method can help identify groups of barley families with different salinity tolerant abilities.
Collapse
Affiliation(s)
- Wu Wang
- Center for Applied Statistics and School of Statistics, Renmin University of China, Beijing, China
| | - Ying Sun
- Statistics Program, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
| | - Huixia Judy Wang
- Department of Statistics, The George Washington University, Washington, DC, USA
| |
Collapse
|
4
|
Guo S, Qiao X. On consistency and sparsity for high-dimensional functional time series with application to autoregressions. BERNOULLI 2023. [DOI: 10.3150/22-bej1464] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- 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
| |
Collapse
|
5
|
Xue K, Yang J, Yao F. Optimal linear discriminant analysis for high-dimensional functional data. J Am Stat Assoc 2023. [DOI: 10.1080/01621459.2022.2164288] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Kaijie Xue
- School of Statistics and Data Science, Nankai University, Tianjin, China
| | - Jin Yang
- Biostatistics and Bioinformatics Branch, Eunice Kennedy Shriver, National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD 20852, U.S.A
| | - Fang Yao
- Department of Probability and Statistics, School of Mathematical Sciences, Center for Statistical Science, Peking University, Beijing, China
| |
Collapse
|
6
|
Liu Y, Wang Z, Tian M, Yu K. Estimation and variable selection for generalized functional partially varying coefficient hybrid models. Stat Pap (Berl) 2022. [DOI: 10.1007/s00362-022-01383-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
|
7
|
Wang Q, Guo S, Yao F, Zou C. Thresholding mean test for functional data with power enhancement. Stat (Int Stat Inst) 2022. [DOI: 10.1002/sta4.509] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Affiliation(s)
- Qingsong Wang
- Institute of Statistics and Big Data Renmin University of China Beijing China
| | - Shaojun Guo
- Institute of Statistics and Big Data Renmin University of China Beijing China
| | - Fang Yao
- School of Mathematical Sciences, Center for Statistical Science Peking University Beijing China
| | - Changliang Zou
- School of Statistics and Data Science LPMC, KLMDASR and LEBPS, Nankai University Tianjin China
| |
Collapse
|
8
|
Subgroup analysis for high-dimensional functional regression. J MULTIVARIATE ANAL 2022. [DOI: 10.1016/j.jmva.2022.105100] [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]
|
9
|
Sang P, Kashlak AB, Kong L. A reproducing kernel Hilbert space framework for functional classification. J Comput Graph Stat 2022. [DOI: 10.1080/10618600.2022.2138407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/31/2022]
Affiliation(s)
- Peijun Sang
- Department of Statistics and Actuarial Science, University of Waterloo
| | - Adam B Kashlak
- Department of Mathematical and Statistical Sciences, University of Alberta
| | - Linglong Kong
- Department of Mathematical and Statistical Sciences, University of Alberta
| |
Collapse
|
10
|
Liu Y, Li Y, Carroll RJ, Wang N. Predictive Functional Linear Models with Diverging Number of Semiparametric Single-Index Interactions. JOURNAL OF ECONOMETRICS 2022; 230:221-239. [PMID: 36017081 PMCID: PMC9398183 DOI: 10.1016/j.jeconom.2021.03.010] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
When predicting crop yield using both functional and multivariate predictors, the prediction performances benefit from the inclusion of the interactions between the two sets of predictors. We assume the interaction depends on a nonparametric, single-index structure of the multivariate predictor and reduce each functional predictor's dimension using functional principal component analysis (FPCA). Allowing the number of FPCA scores to diverge to infinity, we consider a sequence of semiparametric working models with a diverging number of predictors, which are FPCA scores with estimation errors. We show that the parametric component of the model is root-n consistent and asymptotically normal, the overall prediction error is dominated by the estimation of the nonparametric interaction function, and justify a CV-based procedure to select the tuning parameters.
Collapse
Affiliation(s)
- Yanghui Liu
- School of Economics and Statistics, Guangzhou University, China
| | - Yehua Li
- Department of Statistics, University of California, Riverside, CA, 92521, USA
| | - Raymond J Carroll
- Department of Statistics, Texas A&M University, College Station, TX 77843-3143, and School of Mathematical and Physical Sciences, University of Technology Sydney, Broadway NSW 2007, Australia
| | - Naisyin Wang
- Department of Statistics, University of Michigan, Ann Arbor, MI 48109, USA
| |
Collapse
|
11
|
Tang Q, Tu W, Kong L. Estimation for partial functional partially linear additive model. Comput Stat Data Anal 2022. [DOI: 10.1016/j.csda.2022.107584] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
|
12
|
Hu YP, Liang HY. Empirical likelihood in single-index partially functional linear model with missing observations. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2022.2094413] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Yan-Ping Hu
- School of Mathematical Sciences, Tongji University, Shanghai, P.R. China
| | - Han-Ying Liang
- School of Mathematical Sciences, Tongji University, Shanghai, P.R. China
| |
Collapse
|
13
|
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
| |
Collapse
|
14
|
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]
|
15
|
Wang B, Zhang B, Yan H. Functional sufficient dimension reduction based on weighted method. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2022.2087878] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Bingcan Wang
- School of Statistics, Capital University of Economics and Business, Beijing, China
| | - Baoxue Zhang
- School of Statistics, Capital University of Economics and Business, Beijing, China
| | - Haibo Yan
- School of Public Administration, Jinan University, Guangzhou, China
| |
Collapse
|
16
|
Bindele HF, Denhere M, Sun W. Generalized signed-rank estimation and selection for the functional linear model. STATISTICS-ABINGDON 2022. [DOI: 10.1080/02331888.2022.2084094] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Huybrechts F. Bindele
- Department of Mathematics and Statistics, University of South Alabama, Mobile, AL, USA
| | | | - Wei Sun
- Auburn University, Auburn, AL, USA
| |
Collapse
|
17
|
Li C, Xiao L, Luo S. Joint model for survival and multivariate sparse functional data with application to a study of Alzheimer's Disease. Biometrics 2022; 78:435-447. [PMID: 33501651 PMCID: PMC8310894 DOI: 10.1111/biom.13427] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Revised: 11/06/2020] [Accepted: 01/08/2021] [Indexed: 11/29/2022]
Abstract
Studies of Alzheimer's disease (AD) often collect multiple longitudinal clinical outcomes, which are correlated and predictive of AD progression. It is of great scientific interest to investigate the association between the outcomes and time to AD onset. We model the multiple longitudinal outcomes as multivariate sparse functional data and propose a functional joint model linking multivariate functional data to event time data. In particular, we propose a multivariate functional mixed model to identify the shared progression pattern and outcome-specific progression patterns of the outcomes, which enables more interpretable modeling of associations between outcomes and AD onset. The proposed method is applied to the Alzheimer's Disease Neuroimaging Initiative study (ADNI) and the functional joint model sheds new light on inference of five longitudinal outcomes and their associations with AD onset. Simulation studies also confirm the validity of the proposed model. Data used in preparation of this article were obtained from the ADNI database.
Collapse
Affiliation(s)
- Cai Li
- Department of Biostatistics, Yale University, New Haven, Connecticut, USA
| | - Luo Xiao
- Department of Statistics, North Carolina State University, Raleigh, North Carolina, USA
| | - Sheng Luo
- Department of Biostatistics and Bioinformatics, Duke University, Durham, North Carolina, USA
| |
Collapse
|
18
|
Zhou Y, Zhang W, Lin H, Lian H. Partially linear functional quantile regression in a reproducing kernel Hilbert space. J Nonparametr Stat 2022. [DOI: 10.1080/10485252.2022.2073354] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Yan Zhou
- College of Mathematics and Statistics, Institute of Statistical Sciences, Shenzhen University, Shenzhen, People's Republic of China
| | - Weiping Zhang
- Department of Statistics, USTC, Hefei, People's Republic of China
| | - Hongmei Lin
- School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai, People's Republic of China
| | - Heng Lian
- Department of Mathematics, City University of Hong Kong, Hong Kong, People's Republic of China
| |
Collapse
|
19
|
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]
|
20
|
Liang B, Gao T, Bai D, Wang G. Functional dimension reduction based on fuzzy partition and transformation. AUST NZ J STAT 2022. [DOI: 10.1111/anzs.12363] [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]
Affiliation(s)
- Beiting Liang
- School of Economics Jinan University Guangzhou 510632China
| | - Taoxuan Gao
- Office of Scientific R and D Jinan University Guangzhou 510632China
| | - Defa Bai
- Office of Scientific R and D Jinan University Guangzhou 510632China
| | - Guochang Wang
- School of Economics Jinan University Guangzhou 510632China
| |
Collapse
|
21
|
Ma H, Liu C, Xu S, Yang J. Subgroup analysis for functional partial linear regression model. CAN J STAT 2022. [DOI: 10.1002/cjs.11696] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Haiqiang Ma
- School of Statistics Jiangxi University of Finance and Economics Nanchang Jiangxi 330013 China
| | - Chao Liu
- Department of Statistics and Data Science The Southern University of Science and Technology Shenzhen Guangdong 518055 China
| | - Sheng Xu
- Department of Applied Mathematics The Hong Kong Polytechnic University Kowloon, Hong Kong (SAR) China
| | - Jin Yang
- Biostatistics and Bioinformatics Branch Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health Bethesda MD 20817 U.S.A
| |
Collapse
|
22
|
ZHU H, LI Y, LIU B, YAO W, ZHANG R. Extreme quantile estimation for partial functional linear regression models with heavy-tailed distributions. CAN J STAT 2022; 50:267-286. [PMID: 38239624 PMCID: PMC10795494 DOI: 10.1002/cjs.11653] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2020] [Accepted: 03/15/2021] [Indexed: 11/10/2022]
Abstract
In this article, we propose a novel estimator of extreme conditional quantiles in partial functional linear regression models with heavy-tailed distributions. The conventional quantile regression estimators are often unstable at the extreme tails due to data sparsity, especially for heavy-tailed distributions. We first estimate the slope function and the partially linear coefficient using a functional quantile regression based on functional principal component analysis, which is a robust alternative to the ordinary least squares regression. The extreme conditional quantiles are then estimated by using a new extrapolation technique from extreme value theory. We establish the asymptotic normality of the proposed estimator and illustrate its finite sample performance by simulation studies and an empirical analysis of diffusion tensor imaging data from a cognitive disorder study.
Collapse
Affiliation(s)
- Hanbing ZHU
- School of Statistics, Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE, East China Normal University, Shanghai, China
| | - Yehua LI
- Department of Statistics, University of California, Riverside, California, USA
| | - Baisen LIU
- School of Statistics, Dongbei University of Finance and Economics, Dalian, China
| | - Weixin YAO
- Department of Statistics, University of California, Riverside, California, USA
| | - Riquan ZHANG
- School of Statistics, Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE, East China Normal University, Shanghai, China
| |
Collapse
|
23
|
|
24
|
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]
|
25
|
Zou Y, Wu C, Fan G, Zhang R. Estimation for a hybrid model of functional and linear measurement errors regression with missing response. STATISTICS-ABINGDON 2022. [DOI: 10.1080/02331888.2022.2038166] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Yuye Zou
- College of Economics and Management, Shanghai Maritime University, Shanghai, People's Republic of China
- Key Laboratory of Advanced Theory and Application in Statistics and Data Science – MOE, School of Statistics, East China Normal University, Shanghai, People's Republic of China
| | - Chengxin Wu
- School of Mathematics, Hefei University of Technology, Hefei, People's Republic of China
- School of Mathematics and Statistics, Huangshan University, Huangshan, People's Republic of China
| | - Guoliang Fan
- College of Economics and Management, Shanghai Maritime University, Shanghai, People's Republic of China
| | - Riquan Zhang
- Key Laboratory of Advanced Theory and Application in Statistics and Data Science – MOE, School of Statistics, East China Normal University, Shanghai, People's Republic of China
| |
Collapse
|
26
|
Liang D, Huang H, Guan Y, Yao F. Test of Weak Separability for Spatially Stationary Functional Field. J Am Stat Assoc 2022. [DOI: 10.1080/01621459.2021.2002156] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Decai Liang
- School of Statistics and Data Science, LPMC and KLMDASR, Nankai University, Tianjin, China
| | - Hui Huang
- School of Mathematics, Sun Yat-sen University, Guangzhou, China
| | - Yongtao Guan
- Department of Management Science, University of Miami, Coral Gables, FL
| | - Fang Yao
- School of Mathematical Sciences, Center for Statistical Science, Peking University, Beijing, China
| |
Collapse
|
27
|
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
| |
Collapse
|
28
|
Generalized partially functional linear model. Sci Rep 2021; 11:23428. [PMID: 34873245 PMCID: PMC8648855 DOI: 10.1038/s41598-021-02896-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2021] [Accepted: 11/22/2021] [Indexed: 11/24/2022] Open
Abstract
In this paper, a generalized partially functional linear regression model is proposed and the asymptotic property of the proposed estimated coefficients in the model is established. Extensive simulation experiment results are consistent with the theoretical result. Finally, two application examples of the model are given. One is sleep quality study where we studied the effects of heart rate, percentage of sleep time on total sleep in bed, wake after sleep onset and number of wakening during the night on sleep quality in 22 healthy people. The other one is mortality rate where we studied the effects of air quality index, temperature, relative humidity, GDP per capita and the number of beds per thousand people on the mortality rate across 80 major cities in China.
Collapse
|
29
|
Pan Y, Laber EB, Smith MA, Zhao YQ. Reinforced risk prediction with budget constraint using irregularly measured data from electronic health records. J Am Stat Assoc 2021; 118:1090-1101. [PMID: 37333855 PMCID: PMC10274334 DOI: 10.1080/01621459.2021.1978467] [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] [Received: 08/23/2019] [Revised: 03/10/2021] [Accepted: 08/29/2021] [Indexed: 10/20/2022]
Abstract
Uncontrolled glycated hemoglobin (HbA1c) levels are associated with adverse events among complex diabetic patients. These adverse events present serious health risks to affected patients and are associated with significant financial costs. Thus, a high-quality predictive model that could identify high-risk patients so as to inform preventative treatment has the potential to improve patient outcomes while reducing healthcare costs. Because the biomarker information needed to predict risk is costly and burdensome, it is desirable that such a model collect only as much information as is needed on each patient so as to render an accurate prediction. We propose a sequential predictive model that uses accumulating patient longitudinal data to classify patients as: high-risk, low-risk, or uncertain. Patients classified as high-risk are then recommended to receive preventative treatment and those classified as low-risk are recommended to standard care. Patients classified as uncertain are monitored until a high-risk or low-risk determination is made. We construct the model using claims and enrollment files from Medicare, linked with patient Electronic Health Records (EHR) data. The proposed model uses functional principal components to accommodate noisy longitudinal data and weighting to deal with missingness and sampling bias. The proposed method demonstrates higher predictive accuracy and lower cost than competing methods in a series of simulation experiments and application to data on complex patients with diabetes.
Collapse
Affiliation(s)
- Yinghao Pan
- Department of Mathematics and Statistics, University of North Carolina at Charlotte
| | - Eric B. Laber
- Department of Statistics, North Carolina State University
| | - Maureen A. Smith
- Departments of Population Health Sciences and Family Medicine, University of Wisconsin-Madison
| | - Ying-Qi Zhao
- Public Health Sciences Division, Fred Hutchinson Cancer Research Center
| |
Collapse
|
30
|
Affiliation(s)
- Ying Yang Fang Yao
- Department of Probability and Statistics, School of Mathematical Sciences, Center for Statistical Science, Peking University, Beijing, China
| |
Collapse
|
31
|
Hu Y, Wang Y, Zhang L, Xue L. Statistical inference of varying-coefficient partial functional spatial autoregressive model. COMMUN STAT-THEOR M 2021. [DOI: 10.1080/03610926.2021.1992438] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Yuping Hu
- School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China
| | - Yilun Wang
- School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China
| | - Liying Zhang
- School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China
| | - Liugen Xue
- College of Applied Sciences, Beijing University of Technology, Beijing, China
| |
Collapse
|
32
|
Jiang J, Lin H, Zhong Q, Li Y. Analysis of multivariate non-gaussian functional data: A semiparametric latent process approach. J MULTIVARIATE ANAL 2021. [DOI: 10.1016/j.jmva.2021.104888] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
|
33
|
Zhang X, Fang K, Zhang Q. Multivariate functional generalized additive models. J STAT COMPUT SIM 2021. [DOI: 10.1080/00949655.2021.1979550] [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]
Affiliation(s)
- Xiaochen Zhang
- Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan, People's Republic of China
| | - Kuangnan Fang
- Department of Statistics and Data Science, School of Economics, Xiamen University, Xiamen, People's Republic of China
| | - Qingzhao Zhang
- Department of Statistics and Data Science, School of Economics, Xiamen University, Xiamen, People's Republic of China
- The Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, People's Republic of China
| |
Collapse
|
34
|
|
35
|
Gan J, Peng Z, Zhu X, Hu R, Ma J, Wu G. Brain functional connectivity analysis based on multi-graph fusion. Med Image Anal 2021; 71:102057. [PMID: 33957559 PMCID: PMC8934107 DOI: 10.1016/j.media.2021.102057] [Citation(s) in RCA: 23] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2020] [Revised: 03/25/2021] [Accepted: 03/27/2021] [Indexed: 12/13/2022]
Abstract
In this paper, we propose a framework for functional connectivity network (FCN) analysis, which conducts the brain disease diagnosis on the resting state functional magnetic resonance imaging (rs-fMRI) data, aiming at reducing the influence of the noise, the inter-subject variability, and the heterogeneity across subjects. To this end, our proposed framework investigates a multi-graph fusion method to explore both the common and the complementary information between two FCNs, i.e., a fully-connected FCN and a 1 nearest neighbor (1NN) FCN, whereas previous methods only focus on conducting FCN analysis from a single FCN. Specifically, our framework first conducts the graph fusion to produce the representation of the rs-fMRI data with high discriminative ability, and then employs the L1SVM to jointly conduct brain region selection and disease diagnosis. We further evaluate the effectiveness of the proposed framework on various data sets of the neuro-diseases, i.e., Fronto-Temporal Dementia (FTD), Obsessive-Compulsive Disorder (OCD), and Alzheimers Disease (AD). The experimental results demonstrate that the proposed framework achieves the best diagnosis performance via selecting reasonable brain regions for the classification tasks, compared to state-of-the-art FCN analysis methods.
Collapse
Affiliation(s)
- Jiangzhang Gan
- Center for Future Media and School of Computer Science and Technology, University of Electronic Science and Technology of China, Chengdu 611731, China; School of natural and Computational Science, Massey University Auckland Campus, Auckland 0745, New Zealand
| | - Ziwen Peng
- Center for the Study of Applied Psychology, Guangdong Key Laboratory of Mental Health and Cognitive Science and School of Psychology, South China Normal University, Guangzhou 510631, China
| | - Xiaofeng Zhu
- Center for Future Media and School of Computer Science and Technology, University of Electronic Science and Technology of China, Chengdu 611731, China; School of natural and Computational Science, Massey University Auckland Campus, Auckland 0745, New Zealand
| | - Rongyao Hu
- School of natural and Computational Science, Massey University Auckland Campus, Auckland 0745, New Zealand
| | - Junbo Ma
- Department of Psychiatry, University of North Carolina, Chapel Hill, NC 27599, USA
| | - Guorong Wu
- Department of Psychiatry, University of North Carolina, Chapel Hill, NC 27599, USA; Department of Computer Science, University of North Carolina, Chapel Hill, NC 27599, USA
| |
Collapse
|
36
|
|
37
|
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]
|
38
|
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]
|
39
|
Shi H, Dong J, Wang L, Cao J. Functional principal component analysis for longitudinal data with informative dropout. Stat Med 2020; 40:712-724. [PMID: 33179286 DOI: 10.1002/sim.8798] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2020] [Revised: 08/21/2020] [Accepted: 10/14/2020] [Indexed: 11/11/2022]
Abstract
In longitudinal studies, the values of biomarkers are often informatively missing due to dropout. The conventional functional principal component analysis typically disregards the missing information and simply treats the unobserved data points as missing completely at random. As a result, the estimation of the mean function and the covariance surface might be biased, resulting in a biased estimation of the functional principal components. We propose the informatively missing functional principal component analysis (imFunPCA), which is well suited for cases where the longitudinal trajectories are subject to informative missingness. Computation of the functional principal components in our approach is based on the likelihood of the data, where information of both the observed and missing data points are incorporated. We adopt a regression-based orthogonal approximation method to decompose the latent stochastic process based on a set of orthonormal empirical basis functions. Under the case of informative missingness, we show via simulation studies that the performance of our approach is superior to that of the conventional ones. We apply our method on a longitudinal dataset of kidney glomerular filtration rates for patients post renal transplantation.
Collapse
Affiliation(s)
- Haolun Shi
- Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, British Columbia, Canada
| | - Jianghu Dong
- Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, British Columbia, Canada.,Department of Biostatistics & Division of Nephrology, University of Nebraska Medical Center, Nebraska, USA
| | - Liangliang Wang
- Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, British Columbia, Canada
| | - Jiguo Cao
- Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, British Columbia, Canada
| |
Collapse
|
40
|
Abstract
Summary
Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. We investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly, and often much, shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.
Collapse
Affiliation(s)
- Zhenhua Lin
- Department of Statistics and Applied Probability, National University of Singapore, 6 Science Drive, 117546, Singapore
| | - Jane-Ling Wang
- Department of Statistics, University of California, One Shields Avenue, Davis, California 95616, U.S.A
| | - Qixian Zhong
- Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
| |
Collapse
|
41
|
Dai X, Lin Z, Müller HG. Modeling sparse longitudinal data on Riemannian manifolds. Biometrics 2020; 77:1328-1341. [PMID: 33034049 DOI: 10.1111/biom.13385] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2020] [Revised: 07/14/2020] [Accepted: 09/15/2020] [Indexed: 11/28/2022]
Abstract
Modern data collection often entails longitudinal repeated measurements that assume values on a Riemannian manifold. Analyzing such longitudinal Riemannian data is challenging, because of both the sparsity of the observations and the nonlinear manifold constraint. Addressing this challenge, we propose an intrinsic functional principal component analysis for longitudinal Riemannian data. Information is pooled across subjects by estimating the mean curve with local Fréchet regression and smoothing the covariance structure of the linearized data on tangent spaces around the mean. Dimension reduction and imputation of the manifold-valued trajectories are achieved by utilizing the leading principal components and applying best linear unbiased prediction. We show that the proposed mean and covariance function estimates achieve state-of-the-art convergence rates. For illustration, we study the development of brain connectivity in a longitudinal cohort of Alzheimer's disease and normal participants by modeling the connectivity on the manifold of symmetric positive definite matrices with the affine-invariant metric. In a second illustration for irregularly recorded longitudinal emotion compositional data for unemployed workers, we show that the proposed method leads to nicely interpretable eigenfunctions and principal component scores. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative database.
Collapse
Affiliation(s)
- Xiongtao Dai
- Department of Statistics, Iowa State University, Ames, Iowa
| | - Zhenhua Lin
- Department of Statistics and Applied Probability, National University of Singapore, Singapore
| | - Hans-Georg Müller
- Department of Statistics, University of California, Davis, California
| |
Collapse
|
42
|
Abstract
Functional regression allows for a scalar response to be dependent on a functional predictor; however, not much work has been done when response variables are dependence spatial variables. In this paper, we introduce a new partial functional linear spatial autoregressive model which explores the relationship between a scalar dependence spatial response variable and explanatory variables containing both multiple real-valued scalar variables and a function-valued random variable. By means of functional principal components analysis and the instrumental variable estimation method, we obtain the estimators of the parametric component and slope function of the model. Under some regularity conditions, we establish the asymptotic normality for the parametric component and the convergence rate for slope function. At last, we illustrate the finite sample performance of our proposed methods with some simulation studies.
Collapse
|
43
|
Yang SJ, Shin H, Lee SH, Lee S. Functional linear regression model with randomly censored data: Predicting conversion time to Alzheimer ’s disease. Comput Stat Data Anal 2020. [DOI: 10.1016/j.csda.2020.107009] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
44
|
|
45
|
|
46
|
Rank method for partial functional linear regression models. J Korean Stat Soc 2020. [DOI: 10.1007/s42952-020-00075-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
47
|
Jiang R, Wang L, Bai Y. Optimal model averaging estimator for semi-functional partially linear models. METRIKA 2020. [DOI: 10.1007/s00184-020-00772-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
|
48
|
Robust estimation with a modified Huber’s loss for partial functional linear models based on splines. J Korean Stat Soc 2020. [DOI: 10.1007/s42952-020-00052-x] [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]
|
49
|
|
50
|
|