Problems in large-scale estimation

Barbehenn, Alton

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

Description

Title

Problems in large-scale estimation

Author(s)

Barbehenn, Alton

Issue Date

2023-04-12

Director of Research (if dissertation) or Advisor (if thesis)

Zhao, Sihai D

Doctoral Committee Chair(s)

Zhao, Sihai D

Committee Member(s)

• Koenker, Roger
• Liang, Feng
• Zhu, Ruoqing

Department of Study

Statistics

Discipline

Statistics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

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

Abstract

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.

Graduation Semester

2023-05

Type of Resource

Thesis

Copyright and License Information

Copyright 2023 Alton Barbehenn

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