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

Zhang, Yi

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

Description

Title

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

Author(s)

Zhang, Yi

Issue Date

2025-05-30

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

• Shao, Xiaofeng
• Yang, Yun

Doctoral Committee Chair(s)

Shao, Xiaofeng

Committee Member(s)

• Zhu, Ruoqing
• Fellouris, Georgios

Department of Study

Statistics

Discipline

Statistics

Degree Granting Institution

University of Illinois Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

Self Normalization, Machine Learning, Time Series, Nonparametric Statistics

Abstract

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.

Graduation Semester

2025-08

Type of Resource

Thesis

Handle URL

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

Copyright and License Information

Copyright 2025 Yi Zhang

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