2026-09-20T21:33:03Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/115577 2023-07-11 col_2142_5131 col_2142_17362 com_2142_5130 com_2142_17361 com_2142_8903

Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-05-01 The student, Huiqin Xin, accepted the attached license on 2022-04-18 at 20:55. The student, Huiqin Xin, submitted this Dissertation for approval on 2022-04-18 at 21:03. This Dissertation was approved for publication on 2022-04-22 at 07:53. DSpace SAF Submission Ingestion Package generated from Vireo submission #17773 on 2022-11-11 at 12:06:08 Zhao, Sihai Dave Zhao, Sihai Dave Liang, Feng Chatterjee, Sabyasachi Wang, Shulei 2022-05 application/pdf en text Simultaneous multiparameter estimation Xin, Huiqin 2022-04-22 Compressive sensing Compound decision theory Machine learning Simultaneously estimating a large amount of parameters is a common problem in statistics. We investigate two cases of simultaneous multiparameter estimation. In the first case, data are generated directly by target parameters. Our research focuses on high-dimensional covariance matrix estimation problem. We introduce two empirical Bayes approaches, compound decision approach and regression approach, to solve this problem. In both approaches, we vectorize the covariance matrices and approximate the optimal decision rule in a broad class of rules. In the second case, data are generated by a function of the target parameters with addictive observation noise. In particular, we study the linear model where the target nonnegative sparse vector is transformed to noisy observations by a measurement matrix. Specifically, the designed measurement matrix is corrupted in data generation. We investigate the behavior of matrix uncertainty selector in the corrupted matrix setting and weakened its condition with nonnegativity constraints. Thesis eng https://hdl.handle.net/2142/115577 Copyright 2022 Huiqin Xin Ph.D. Dissertation Statistics University of Illinois at Urbana-Champaign Statistics