{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/125689"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/125689","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Nonparametric testing in modern statistics: A personal journey","abstract":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2026-08-01","abstract_html":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2026-08-01","abstract_has_math":false,"creators":["Gao, Hanjia"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Statistics","degree_department":null,"school":null,"contributors":["Shao, Xiaofeng","Yang, Yun","Simpson, Douglas","Wang, Yuexi"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-07-05","date_published":"2024-07-05","updated_at":"2026-07-22T22:25:02Z","subjects":["Nonparametric Testing","High-dimensional Statistics","Functional Data","Time Series"],"languages":["en","eng"],"rights":["Copyright 2024 Hanjia Gao"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/125689","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Shao, Xiaofeng","Yang, Yun","Simpson, Douglas","Wang, Yuexi"]},{"key":"dc:creator","label":"Author","values":["Gao, Hanjia"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2024-07-05","2024-08"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Nonparametric Testing","High-dimensional Statistics","Functional Data","Time Series"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2024 Hanjia Gao"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/125689"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2026-08-01","The student, Hanjia Gao, accepted the attached license on 2024-07-03 at 15:16.","The student, Hanjia Gao, submitted this Dissertation for approval on 2024-07-03 at 15:28.","This Dissertation was approved for publication on 2024-07-05 at 07:10.","DSpace SAF Submission Ingestion Package generated from Vireo submission #20939 on 2025-02-04 at 21:16:17","Nonparametric testing is a fundamental branch of statistics and has numerous applications in modern statistics. This thesis is based on four projects in which we study four different nonparametric testing problems. In the first project, we study the two-sample test and aim to test the equality of two high-dimensional distributions. In particular, we propose a novel studentized test statistic based on the maximum mean discrepancy and establish the asymptotic theory of the proposed test in the high dimensional setting. In the second project, we investigate the change point testing problem for vector-valued time series with both temporal and cross-sectional dependence. By integrating the idea of sample splitting and self-normalization, we propose a dimension-agnostic testing method applicable to low-, medium-, and high dimensional settings, and provide the asymptotic properties of the proposed test both under the null and against the local alternatives. In the third project, we focus on functional time series inference and generalize our test proposed in the previous project to the infinite-dimensional setting. In particular, we propose a fully functional approach based on sample splitting and illustrate it for several testing problems. In the fourth project, we consider the two-sample conditional distribution test and propose a new population-level metric that characterizes the discrepancy between two conditional distributions. We also construct a test statistic using generative adversarial networks and introduce a multiplier bootstrap procedure to approximate the critical value. The asymptotic theory is provided under the null and against the local alternatives, and some preliminary simulations are presented to demonstrate the effectiveness of the test."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Nonparametric testing in modern statistics: A personal journey"]}]}],"canonical_facts":{"dc:contributor":["Shao, Xiaofeng","Yang, Yun","Simpson, Douglas","Wang, Yuexi"],"dc:creator":["Gao, Hanjia"],"dc:date":["2024-07-05","2024-08"],"dc:description":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2026-08-01","The student, Hanjia Gao, accepted the attached license on 2024-07-03 at 15:16.","The student, Hanjia Gao, submitted this Dissertation for approval on 2024-07-03 at 15:28.","This Dissertation was approved for publication on 2024-07-05 at 07:10.","DSpace SAF Submission Ingestion Package generated from Vireo submission #20939 on 2025-02-04 at 21:16:17","Nonparametric testing is a fundamental branch of statistics and has numerous applications in modern statistics. This thesis is based on four projects in which we study four different nonparametric testing problems. In the first project, we study the two-sample test and aim to test the equality of two high-dimensional distributions. In particular, we propose a novel studentized test statistic based on the maximum mean discrepancy and establish the asymptotic theory of the proposed test in the high dimensional setting. In the second project, we investigate the change point testing problem for vector-valued time series with both temporal and cross-sectional dependence. By integrating the idea of sample splitting and self-normalization, we propose a dimension-agnostic testing method applicable to low-, medium-, and high dimensional settings, and provide the asymptotic properties of the proposed test both under the null and against the local alternatives. In the third project, we focus on functional time series inference and generalize our test proposed in the previous project to the infinite-dimensional setting. In particular, we propose a fully functional approach based on sample splitting and illustrate it for several testing problems. In the fourth project, we consider the two-sample conditional distribution test and propose a new population-level metric that characterizes the discrepancy between two conditional distributions. We also construct a test statistic using generative adversarial networks and introduce a multiplier bootstrap procedure to approximate the critical value. The asymptotic theory is provided under the null and against the local alternatives, and some preliminary simulations are presented to demonstrate the effectiveness of the test."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/125689"],"dc:language":["en","eng"],"dc:rights":["Copyright 2024 Hanjia Gao"],"dc:subject":["Nonparametric Testing","High-dimensional Statistics","Functional Data","Time Series"],"dc:title":["Nonparametric testing in modern statistics: A personal journey"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:02Z"}