Statistical inference with complex datasets: from self normalization to machine learning

This thesis is based on four projects I did to develop reliable inferential tools for complex datasets during my PhD study. I started working on this problem by considering bandwidth free hypothesis testing for time series data, resulting in a self normalization based test procedure that greatly reduces the size distortion of existing tests for multi-dimensional parameters. With the intuition and novel theoretical tools gained, I then considered the hypothesis testing problem for functional (i.e., infinite-dimensional) parameters and for metric space valued time series, leading to several new tests, as there was a lack of bandwidth free tests for these data types. By leveraging modern machine learning tools such as deep neural network and generative neural network, I also worked on developing new tests for some traditional statistical testing problems, with the goal of accommodating both low- and high-dimensional data. Examples include new nonparametric conditional independence tests that work well when the conditioning variable is of high dimension and can have high-dimensional data (e.g., texts and images) as the covariates of interests and/or the response.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Zhang, Yi

Contributors dc:contributor

• Shao, Xiaofeng
• Yang, Yun
• Zhu, Ruoqing
• Fellouris, Georgios

• Self Normalization
• Machine Learning
• Time Series
• Nonparametric Statistics

Statement dc:rights

• Copyright 2025 Yi Zhang

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/129818

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F129818