Simultaneous multiparameter estimation

Xin, Huiqin

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https://hdl.handle.net/2142/115577 Copy

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.

Graduation Semester

2022-05

Type of Resource

Thesis

Copyright and License Information

Copyright 2022 Huiqin Xin

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