2026-09-18T23:18:01Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/129818 2025-10-25 col_2142_5131 col_2142_17362 com_2142_5130 com_2142_17361 com_2142_8903

application/pdf en text Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms The student, Yi Zhang, accepted the attached license on 2025-05-28 at 12:45. The student, Yi Zhang, submitted this Dissertation for approval on 2025-05-28 at 12:52. This Dissertation was approved for publication on 2025-05-30 at 10:32. DSpace SAF Submission Ingestion Package generated from Vireo submission #22313 on 2025-10-20 at 16:57:04 Statistical inference with complex datasets: from self normalization to machine learning Zhang, Yi 2025-05-30 Shao, Xiaofeng Yang, Yun Shao, Xiaofeng Zhu, Ruoqing Fellouris, Georgios Self Normalization Machine Learning Time Series Nonparametric Statistics eng 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. 2025-08 Text https://hdl.handle.net/2142/129818 Copyright 2025 Yi Zhang Statistics Statistics University of Illinois Urbana-Champaign Ph.D. Dissertation