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Zhao, Sihai Dave Zhao, Sihai Dave Liang, Feng Eck, Daniel J Zhu, Ruoqing Wang, Yihe 2021-09-17T04:04:05Z 2021-09-17T04:04:05Z 2023-09-17T04:07:01Z 2021-03-30 2021-05 Large-scale multivariate regression has various applications in machine learning fields, especially in image recognition, gene expression prediction and multivariate time series prediction. Numerous approaches have been developed to solve this problem. Some popular statistical methods are group lasso and multivariate ridge regression. Most existing methods either leverage the information of the error covariance matrix or assume specific parameter structures. However, in practice, this information is not available. To resolve these issues, we start with formulating multivariate regression as a compound decision problem. In Chapter 2, we propose an empirical Bayes-based approach where the prior distribution of unknown parameters is estimated nonparametrically from the data. Unlike existing methods, the proposed method does not assume any structure of parameters. In Chapter 3, we propose a method that linearly shrinks each coordinate of ordinary least squares estimator. Both theoretical and numerical results are available. In Chapter 4, some nonlinear shrinkage methods based on soft threshold operator are also proposed. Taking the advantage of large number of related outcomes, the proposed methods outperform popular existing methods. Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2023-05-01 The student, Yihe Wang, accepted the attached license on 2021-03-26 at 14:14. The student, Yihe Wang, submitted this Dissertation for approval on 2021-03-26 at 14:23. This Dissertation was approved for publication on 2021-03-30 at 09:21. DSpace SAF Submission Ingestion Package generated from Vireo submission #16214 on 2021-09-16 at 20:07:51 Made available in DSpace on 2021-09-17T04:04:05Z (GMT). No. of bitstreams: 2 WANG-DISSERTATION-2021.pdf: 2631668 bytes, checksum: c6bfd606fee117ce49bf41b6c956ee2d (MD5) LICENSE.txt: 4206 bytes, checksum: 80e591243bc13266b37bdf9ef92f5193 (MD5) Previous issue date: 2021-03-30 Embargo set by: Seth Robbins for item 118630 Lift date: 2023-09-17T04:04:53Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 118630 Lift date: 2023-09-17T04:07:01Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system Author requested closed access (OA after 2yrs) in Vireo ETD system Limited application/pdf http://hdl.handle.net/2142/110785 en Copyright 2021 Yihe Wang multivariate regression compound decision nonparametric empirical Bayes Stein's unbiased risk Simultaneous estimation approaches to large-scale multivariate regression text Thesis Statistics Statistics University of Illinois at Urbana-Champaign Dissertation Ph.D.