2026-09-18T20:17:18Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/120242 2023-09-05 col_2142_5131 col_2142_17362 com_2142_5130 com_2142_17361 com_2142_8903

Zhao, Sihai D Zhao, Sihai D Koenker, Roger Liang, Feng Zhu, Ruoqing 2023-05 application/pdf en text Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-09-01 without embargo terms The student, Alton Barbehenn, accepted the attached license on 2023-04-08 at 09:06. The student, Alton Barbehenn, submitted this Dissertation for approval on 2023-04-08 at 09:16. This Dissertation was approved for publication on 2023-04-12 at 14:55. DSpace SAF Submission Ingestion Package generated from Vireo submission #18935 on 2023-09-01 at 17:08:06 Problems in large-scale estimation Barbehenn, Alton 2023-04-12 Empirical Bayes Nonparametric Regression Compound Decision Nonparametric Maximum Likelihood Compound Decision Shrinkage 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. Thesis eng https://hdl.handle.net/2142/120242 Copyright 2023 Alton Barbehenn Ph.D. Dissertation Statistics University of Illinois at Urbana-Champaign Statistics