Advanced search
Publication Cover
Journal of the American Statistical Association Volume 112, 2017 - Issue 519
Submit an article Journal homepage
2,897
Views
99
CrossRef citations to date
0
Altmetric
Theory and Methods

Parsimonious Tensor Response Regression

Lexin LiDivision of Biostatistics, University of California at Berkeley, Berkley, CA
&
Xin ZhangDepartment of Statistics, Florida State University, Tallahassee, FL
Pages 1131-1146 | Received 01 Sep 2015, Published online: 13 Apr 2017

Citations (99)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (26)

Jinwen Liang & Maozai Tian. (2024) Imputed mean tensor regression for near-sited spatial temporal data. Journal of Applied Statistics 51:6, pages 1057-1075.
Read now
Junge Li & Qing Mai. (2024) Model-Based Tensor Low-Rank Clustering. Journal of Computational and Graphical Statistics 33:1, pages 208-218.
Read now
Monica Billio, Roberto Casarin & Matteo Iacopini. (2024) Bayesian Markov-Switching Tensor Regression for Time-Varying Networks. Journal of the American Statistical Association 119:545, pages 109-121.
Read now
Le Zhou, R. Dennis Cook & Hui Zou. (2023) Enveloped Huber Regression. Journal of the American Statistical Association 0:0, pages 1-11.
Read now
Hilda S. Ibriga & Will Wei Sun. (2023) Covariate-Assisted Sparse Tensor Completion. Journal of the American Statistical Association 118:544, pages 2605-2619.
Read now
S. Yaser Samadi & H. M. Wiranthe B. Herath. (2023) Reduced-Rank Envelope Vector Autoregressive Model. Journal of Business & Economic Statistics 0:0, pages 1-27.
Read now
Yifan Li, Chunjie Wu, Wendong Li & Fugee Tsung. (2023) Nonparametric passenger flow monitoring using a minimum distance criterion. IISE Transactions 55:9, pages 861-872.
Read now
Saptarshi Chakraborty & Zhihua Su. (2023) A Comprehensive Bayesian Framework for Envelope Models. Journal of the American Statistical Association 0:0, pages 1-11.
Read now
Jing Zhang, Zhensheng Huang & Zhiqiang Jiang. (2023) Groupwise partial envelope model: efficient estimation in multivariate linear regression. Communications in Statistics - Simulation and Computation 52:7, pages 2924-2940.
Read now
Monica Billio, Roberto Casarin, Matteo Iacopini & Sylvia Kaufmann. (2023) Bayesian Dynamic Tensor Regression. Journal of Business & Economic Statistics 41:2, pages 429-439.
Read now
Jingfei Zhang, Will Wei Sun & Lexin Li. (2023) Generalized Connectivity Matrix Response Regression with Applications in Brain Connectivity Studies. Journal of Computational and Graphical Statistics 32:1, pages 252-262.
Read now
Jie Zhou, Will Wei Sun, Jingfei Zhang & Lexin Li. (2023) Partially Observed Dynamic Tensor Response Regression. Journal of the American Statistical Association 118:541, pages 424-439.
Read now
Qing Mai, Xin Zhang, Yuqing Pan & Kai Deng. (2022) A Doubly Enhanced EM Algorithm for Model-Based Tensor Clustering. Journal of the American Statistical Association 117:540, pages 2120-2134.
Read now
T. Tony Cai, Wenguang Sun & Yin Xia. (2022) LAWS: A Locally Adaptive Weighting and Screening Approach to Spatial Multiple Testing. Journal of the American Statistical Association 117:539, pages 1370-1383.
Read now
Di Wang, Yao Zheng, Heng Lian & Guodong Li. (2022) High-Dimensional Vector Autoregressive Time Series Modeling via Tensor Decomposition. Journal of the American Statistical Association 117:539, pages 1338-1356.
Read now
Jing Zhang & Zhensheng Huang. (2022) Efficient simultaneous partial envelope model in multivariate linear regression. Journal of Statistical Computation and Simulation 92:7, pages 1373-1400.
Read now
Mai Ghannam & Sévérien Nkurunziza. (2022) The risk of tensor Stein-rules in elliptically contoured distributions. Statistics 56:2, pages 421-454.
Read now
Jiaxin Hu, Chanwoo Lee & Miaoyan Wang. (2022) Generalized Tensor Decomposition With Features on Multiple Modes. Journal of Computational and Graphical Statistics 31:1, pages 204-218.
Read now
Sharmistha Guha & Rajarshi Guhaniyogi. (2021) Bayesian Generalized Sparse Symmetric Tensor-on-Vector Regression. Technometrics 63:2, pages 160-170.
Read now
Xiwei Tang, Xuan Bi & Annie Qu. (2020) Individualized Multilayer Tensor Learning With an Application in Imaging Analysis. Journal of the American Statistical Association 115:530, pages 836-851.
Read now
Dehan Kong, Baiguo An, Jingwen Zhang & Hongtu Zhu. (2020) L2RM: Low-Rank Linear Regression Models for High-Dimensional Matrix Responses. Journal of the American Statistical Association 115:529, pages 403-424.
Read now
Yuqing Pan, Qing Mai & Xin Zhang. (2019) Covariate-Adjusted Tensor Classification in High Dimensions. Journal of the American Statistical Association 114:527, pages 1305-1319.
Read now
Hao Yan, Kamran Paynabar & Massimo Pacella. (2019) Structured Point Cloud Data Analysis Via Regularized Tensor Regression for Process Modeling and Optimization. Technometrics 61:3, pages 385-395.
Read now
Xin Zhang & Qing Mai. (2019) Efficient Integration of Sufficient Dimension Reduction and Prediction in Discriminant Analysis. Technometrics 61:2, pages 259-272.
Read now
Aaron J. Molstad & Adam J. Rothman. (2019) A Penalized Likelihood Method for Classification With Matrix-Valued Predictors. Journal of Computational and Graphical Statistics 28:1, pages 11-22.
Read now
Xin Zhang & Lexin Li. (2017) Tensor Envelope Partial Least-Squares Regression. Technometrics 59:4, pages 426-436.
Read now

Articles from other publishers (73)

Lu Li, Xiaofeng Shao & Zhou Yu. (2024) A Slicing‐Free Perspective to Sufficient Dimension Reduction: Selective Review and Recent Developments. International Statistical Review.
Crossref
Daiwei Zhang, Lexin Li, Chandra Sripada & Jian Kang. (2023) Image response regression via deep neural networks. Journal of the Royal Statistical Society Series B: Statistical Methodology 85:5, pages 1589-1614.
Crossref
Zhixin Qi, Hongzhi Wang & Zejiao DongZhixin Qi, Hongzhi Wang & Zejiao Dong. 2024. Dirty Data Processing for Machine Learning. Dirty Data Processing for Machine Learning 39 49 .
Suprateek Kundu, Alec Reinhardt, Serena Song, Joo Han, M. Lawson Meadows, Bruce Crosson & Venkatagiri Krishnamurthy. (2023) Bayesian longitudinal tensor response regression for modeling neuroplasticity. Human Brain Mapping 44:18, pages 6326-6348.
Crossref
R. Dennis Cook, Liliana Forzani & Lan Liu. (2023) Envelopes for multivariate linear regression with linearly constrained coefficients. Scandinavian Journal of Statistics.
Crossref
Mai Ghannam & Sévérien Nkurunziza. (2023) Tensor Stein-rules in a generalized tensor regression model. Journal of Multivariate Analysis 198, pages 105206.
Crossref
Bo Wei, Limin Peng, Ying Guo, Amita Manatunga & Jennifer Stevens. (2023) Tensor Response Quantile Regression with Neuroimaging Data. Biometrics 79:3, pages 1947-1958.
Crossref
Inkoo Lee, Debajyoti Sinha, Qing Mai, Xin Zhang & Dipankar Bandyopadhyay. (2023) Bayesian Regression Analysis of Skewed Tensor Responses. Biometrics 79:3, pages 1814-1825.
Crossref
Xiumin Liu, Lu Niu & Junlong Zhao. (2023) Statistical inference on the significance of rows and columns for matrix-valued data in an additive model. TEST 32:3, pages 785-828.
Crossref
Alessandro Celani & Paolo Pagnottoni. (2023) Matrix autoregressive models: generalization and Bayesian estimation. Studies in Nonlinear Dynamics & Econometrics 0:0.
Crossref
Jinwen Liang, Wolfgang Karl Härdle & Maozai Tian. (2023) Imputed quantile tensor regression for near-sited spatial-temporal data. Computational Statistics & Data Analysis 182, pages 107713.
Crossref
Wentao Qu, Xianchao Xiu, Haifei Zhang & Jun Fan. (2023) An efficient semi-proximal ADMM algorithm for low-rank and sparse regularized matrix minimization problems with real-world applications. Journal of Computational and Applied Mathematics 424, pages 115007.
Crossref
Zhe Cheng, Xiangjian Xu, Zihao Song & Weihua Zhao. (2022) Randomized algorithms for tensor response regression. Statistical Analysis and Data Mining: The ASA Data Science Journal 16:2, pages 149-161.
Crossref
Carlos Llosa-Vite & Ranjan Maitra. (2023) Reduced-Rank Tensor-on-Tensor Regression and Tensor-Variate Analysis of Variance. IEEE Transactions on Pattern Analysis and Machine Intelligence 45:2, pages 2282-2296.
Crossref
Yuehan Yang, Siwei Xia & Hu Yang. (2023) Multivariate sparse Laplacian shrinkage for joint estimation of two graphical structures. Computational Statistics & Data Analysis 178, pages 107620.
Crossref
Yanbo Shen, Yeonhee Park, Saptarshi Chakraborty & Chunming Zhang. (2023) Bayesian Simultaneous Partial Envelope Model with Application to an Imaging Genetics Analysis. The New England Journal of Statistics in Data Science, pages 237-269.
Crossref
Xin Zhang, Kai Deng & Qing Mai. (2023) Envelopes and principal component regression. Electronic Journal of Statistics 17:2.
Crossref
Daniel J. Eck. (2023) General model-free weighted envelope estimation. Electronic Journal of Statistics 17:1.
Crossref
Qing Mai & Xin Zhang. 2023. Springer Handbook of Engineering Statistics. Springer Handbook of Engineering Statistics 817 829 .
Wenxing Guo, Narayanaswamy Balakrishnan & Shanshan Qin. (2023) A modified partial envelope tensor response regression. Stat 12:1.
Crossref
Yue Zhao, Ingrid Van Keilegom & Shanshan Ding. (2022) Envelopes for censored quantile regression. Scandinavian Journal of Statistics 49:4, pages 1562-1585.
Crossref
Chao Ying & Zhou Yu. (2022) Fréchet sufficient dimension reduction for random objects. Biometrika 109:4, pages 975-992.
Crossref
Paul May, Matthew Biesecker & Hossein Moradi Rekabdarkolaee. (2022) Response envelopes for linear coregionalization models. Journal of Multivariate Analysis 192, pages 105015.
Crossref
Yeonhee Park, Zhihua Su & Dongjun Chung. (2022) Envelope‐based partial partial least squares with application to cytokine‐based biomarker analysis for COVID‐19. Statistics in Medicine 41:23, pages 4578-4592.
Crossref
Zerui Tao & Zhouping Li. (2022) Adaptive singular value shrinkage estimate for low rank tensor denoising. Random Matrices: Theory and Applications 11:04.
Crossref
Kai Deng & Xin Zhang. (2021) Tensor envelope mixture model for simultaneous clustering and multiway dimension reduction. Biometrics 78:3, pages 1067-1079.
Crossref
Jiani Liu, Ce Zhu & Yipeng Liu. (2022) Smooth Compact Tensor Ring Regression. IEEE Transactions on Knowledge and Data Engineering 34:9, pages 4439-4452.
Crossref
Lan Liu, Wei Li, Zhihua Su, Dennis Cook, Luca Vizioli & Essa Yacoub. (2021) Efficient estimation via envelope chain in magnetic resonance imaging‐based studies. Scandinavian Journal of Statistics 49:2, pages 481-501.
Crossref
Bradley S. Price, Corban Allenbrand & Ben Sherwood. (2021) Detecting clusters in multivariate response regression. WIREs Computational Statistics 14:3.
Crossref
Rungang Han, Rebecca Willett & Anru R. Zhang. (2022) An optimal statistical and computational framework for generalized tensor estimation. The Annals of Statistics 50:1.
Crossref
Yu Wang, Zeyu Sun, Dogyoon Song & Alfred Hero. (2022) Kronecker-structured covariance models for multiway data. Statistics Surveys 16:none.
Crossref
Mai Ghannam & Sévérien Nkurunziza. (2022) Improved estimation in tensor regression with multiple change-points. Electronic Journal of Statistics 16:2.
Crossref
Keqian Min & Qing Mai. (2022) A general framework for tensor screening through smoothing. Electronic Journal of Statistics 16:1.
Crossref
Rajarshi Guhaniyogi & Daniel Spencer. (2021) Bayesian Tensor Response Regression with an Application to Brain Activation Studies. Bayesian Analysis 16:4.
Crossref
Wei Hu, Tianyu Pan, Dehan Kong & Weining Shen. (2020) Nonparametric matrix response regression with application to brain imaging data analysis. Biometrics 77:4, pages 1227-1240.
Crossref
Giuseppe Brandi & T. Di Matteo. (2021) Predicting multidimensional data via tensor learning. Journal of Computational Science 53, pages 101372.
Crossref
Will Wei Sun, Botao Hao & Lexin Li. 2014. Wiley StatsRef: Statistics Reference Online. Wiley StatsRef: Statistics Reference Online 1 25 .
Jiani Liu, Ce Zhu, Zhen Long, Huyan Huang & Yipeng Liu. (2021) Low-rank tensor ring learning for multi-linear regression. Pattern Recognition 113, pages 107753.
Crossref
Jing Zhang, Zhensheng Huang & Yan Xiong. (2020) Efficient estimation of reduced-rank partial envelope model in multivariate linear regression. Random Matrices: Theory and Applications 10:02, pages 2150024.
Crossref
Xuan Bi, Xiwei Tang, Yubai Yuan, Yanqing Zhang & Annie Qu. (2021) Tensors in Statistics. Annual Review of Statistics and Its Application 8:1, pages 345-368.
Crossref
Linquan Ma, Lan Liu & Wei Yang. (2021) Envelope method with ignorable missing data. Electronic Journal of Statistics 15:2.
Crossref
Zhen Long, Ce Zhu, Jiani Liu & Yipeng Liu. (2021) Bayesian Low Rank Tensor Ring for Image Recovery. IEEE Transactions on Image Processing 30, pages 3568-3580.
Crossref
Ya Zhou, Raymond K. W. Wong & Kejun He. (2021) Tensor Linear Regression: Degeneracy and Solution. IEEE Access 9, pages 7775-7788.
Crossref
Zhixin Qi & Hongzhi Wang. 2021. Database Systems for Advanced Applications. Database Systems for Advanced Applications 88 95 .
Minji Lee & Zhihua Su. (2020) A Review of Envelope Models. International Statistical Review 88:3, pages 658-676.
Crossref
Yipeng Liu, Jiani Liu & Ce Zhu. (2020) Low-Rank Tensor Train Coefficient Array Estimation for Tensor-on-Tensor Regression. IEEE Transactions on Neural Networks and Learning Systems 31:12, pages 5402-5411.
Crossref
X Zhang, C E Lee & X Shao. (2020) Envelopes in multivariate regression models with nonlinearity and heteroscedasticity. Biometrika 107:4, pages 965-981.
Crossref
Daniel Spencer, Rajarshi Guhaniyogi & Raquel Prado. (2020) Joint Bayesian Estimation of Voxel Activation and Inter-regional Connectivity in fMRI Experiments. Psychometrika 85:4, pages 845-869.
Crossref
Rajarshi Guhaniyogi. 2014. Wiley StatsRef: Statistics Reference Online. Wiley StatsRef: Statistics Reference Online 1 18 .
R. Dennis Cook & Liliana Forzani. (2020) Envelopes: A new chapter in partial least squares regression. Journal of Chemometrics 34:10.
Crossref
Botao Hao, Anru Zhang & Guang Cheng. (2020) Sparse and Low-Rank Tensor Estimation via Cubic Sketchings. IEEE Transactions on Information Theory 66:9, pages 5927-5964.
Crossref
Bei Jiang, Eva Petkova, Thaddeus Tarpey & R. Todd Ogden. (2019) A Bayesian approach to joint modeling of matrix‐valued imaging data and treatment outcome with applications to depression studies. Biometrics 76:1, pages 87-97.
Crossref
R. Dennis Cook. (2019) Envelope methods. WIREs Computational Statistics 12:2.
Crossref
来辉 罗. (2020) A Brief Survey on Tensor Regression Model and Its Application. Statistics and Application 09:05, pages 855-861.
Crossref
Yingjie Li, Liangliang Zhang & Tapabrata Maiti. (2020) High dimensional classification for spatially dependent data with application to neuroimaging. Electronic Journal of Statistics 14:2.
Crossref
Tuo Chen, Zhihua Su, Yi Yang & Shanshan Ding. (2020) Efficient estimation in expectile regression using envelope models. Electronic Journal of Statistics 14:1.
Crossref
Anru R. Zhang, Yuetian Luo, Garvesh Raskutti & Ming Yuan. (2020) ISLET: Fast and Optimal Low-Rank Tensor Regression via Importance Sketching. SIAM Journal on Mathematics of Data Science 2:2, pages 444-479.
Crossref
Giuseppe Brandi & Tiziana Di Matteo. 2020. Computational Science – ICCS 2020. Computational Science – ICCS 2020 148 154 .
Rajarshi Guhaniyogi. 2020. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Information Processing and Management of Uncertainty in Knowledge-Based Systems 347 357 .
Yuyang Shi, Linquan Ma & Lan Liu. (2020) Mixed effects envelope models. Stat 9:1.
Crossref
Wenjing Wang, Xin Zhang & Lexin Li. (2019) Common Reducing Subspace Model and Network Alternation Analysis. Biometrics 75:4, pages 1109-1120.
Crossref
Anru Zhang. (2019) Cross: Efficient low-rank tensor completion. The Annals of Statistics 47:2.
Crossref
Xuan Bi, Annie Qu & Xiaotong Shen. (2018) Multilayer tensor factorization with applications to recommender systems. The Annals of Statistics 46:6B.
Crossref
R. Dennis Cook. 2018. An Introduction to Envelopes. An Introduction to Envelopes 273 282 .
Chongliang Luo, Jian Liang, Gen Li, Fei Wang, Changshui Zhang, Dipak K. Dey & Kun Chen. (2018) Leveraging mixed and incomplete outcomes via reduced-rank modeling. Journal of Multivariate Analysis 167, pages 378-394.
Crossref
Laura A. Hatfield & Alan M. Zaslavsky. (2018) Separable covariance models for health care quality measures across years and topics. Statistics in Medicine 37:12, pages 2053-2066.
Crossref
R. Dennis Cook. (2018) Principal Components, Sufficient Dimension Reduction, and Envelopes. Annual Review of Statistics and Its Application 5:1, pages 533-559.
Crossref
R. Dennis Cook & Liliana Forzani. (2017) Big data and partial least‐squares prediction. Canadian Journal of Statistics 46:1, pages 62-78.
Crossref
Eric F. Lock & Gen Li. (2018) Supervised multiway factorization. Electronic Journal of Statistics 12:1.
Crossref
Xin Zhang, Chong Wang & Yichao Wu. (2018) Functional envelope for model-free sufficient dimension reduction. Journal of Multivariate Analysis 163, pages 37-50.
Crossref
Lei Wang & Shanshan Ding. (2018) Vector autoregression and envelope model. Stat 7:1.
Crossref
Yeonhee Park, Zhihua Su & Hongtu Zhu. (2017) Groupwise Envelope Models for Imaging Genetic Analysis. Biometrics 73:4, pages 1243-1253.
Crossref
Christian M. Hafner, Oliver B. Linton & Haihan Tang. (2016) Estimation of a Multiplicative Covariance Structure. SSRN Electronic Journal.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.