Problems in large-scale estimation

Large-scale parameter estimation is of growing importance in many fields where modern data collection tools and procedures encourage the use of massive datasets and models. Compound decision problems come about when the goal is to simultaneously estimate many parameters under a single, unifying loss metric, rather than focusing on each sub-problem individually. In this work we formulate the imputation of censored biomarkers as a compound decision problem, possibly in high dimensions. Nonparametric empirical Bayes g-modeling methods are developed to perform the biomarker imputation. We then turn to the problem of unmixing images used for sub-cellular microscopy, here each pixel represents a small patch that may contain an RNA transcript, the location and identity of which are biologically interesting. Finally, motivated by the difficulties of performing nonparametric empirical Bayes g-modeling methods in high dimensions, we develop a novel nonparametric regression framework that can produce asymptotically optimal estimators without Bayesian arguments.

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

2023

Author dc:creator

• Barbehenn, Alton

Contributors dc:contributor

• Zhao, Sihai D
• Koenker, Roger
• Liang, Feng
• Zhu, Ruoqing

• Empirical Bayes
• Nonparametric Regression
• Compound Decision
• Nonparametric Maximum Likelihood
• Shrinkage

Statement dc:rights

• Copyright 2023 Alton Barbehenn

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/120242

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F120242