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https://hdl.handle.net/2142/115577
Description
Title
Simultaneous multiparameter estimation
Author(s)
Xin, Huiqin
Issue Date
2022-04-22
Director of Research (if dissertation) or Advisor (if thesis)
Zhao, Sihai Dave
Doctoral Committee Chair(s)
Zhao, Sihai Dave
Committee Member(s)
Liang, Feng
Chatterjee, Sabyasachi
Wang, Shulei
Department of Study
Statistics
Discipline
Statistics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Compressive sensing
Compound decision theory
Machine learning
Abstract
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.
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