Simultaneous multiparameter estimation

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Xin, Huiqin

Contributors dc:contributor

• Zhao, Sihai Dave
• Liang, Feng
• Chatterjee, Sabyasachi
• Wang, Shulei

• Compressive sensing
• Compound decision theory
• Machine learning

Statement dc:rights

• Copyright 2022 Huiqin Xin

Language dc:language

en, eng

Handle dc:identifier

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

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F115577