{"id":{"repo_id":"nus","oai_identifier":"oai:scholarbank.nus.edu.sg:10635/14370"},"canonical_url":"https://search.dev.ndltd.org/etd/nus/oai:scholarbank.nus.edu.sg:10635/14370","repository":{"repo_id":"nus","name":"National University of Singapore","base_url":"https://scholarbank.nus.edu.sg/oai/request"},"display":{"title":"Approximating the distributions of x2-type mixtures via matching four cumulants","abstract":"Nonparametric goodness-of-fit tests often result in test statistic which can be written as a random variable of chi-square-type mixtures. Zhang (2003) proposed to approximate its distribution using a random variable of form chi-square-type mixtures via matching the first three cumulants. In this thesis, we attempt to improve this approximation via matching the first four cumulants using a random variable of form non-central chi-square mixtures, resulting in the so-called non-central chi-square-approximation. Application of the results to nonparametric goodness-of-fit test based on local polynomial smoother is investigated. Two simulation studies are conducted to compare the non-central chi-square-approximation, the central chi-square-approximation and the normal approximation numerically. The methodologies are illustrated using a real data example.","abstract_html":"Nonparametric goodness-of-fit tests often result in test statistic which can be written as a random variable of chi-square-type mixtures. Zhang (2003) proposed to approximate its distribution using a random variable of form chi-square-type mixtures via matching the first three cumulants. In this thesis, we attempt to improve this approximation via matching the first four cumulants using a random variable of form non-central chi-square mixtures, resulting in the so-called non-central chi-square-approximation. Application of the results to nonparametric goodness-of-fit test based on local polynomial smoother is investigated. Two simulation studies are conducted to compare the non-central chi-square-approximation, the central chi-square-approximation and the normal approximation numerically. The methodologies are illustrated using a real data example.","abstract_has_math":false,"creators":["LIANG YU"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2004,"date_issued":"2004-12-01","date_published":"2004-12-01","updated_at":"2026-07-24T03:31:51Z","subjects":["x2-type mixtures;Local Polynomial Smoothing;Nonparametric Goodness-of-fit Test"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["LIANG YU"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2004-12-01"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://scholarbank.nus.edu.sg/handle/10635/14370"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["x2-type mixtures;Local Polynomial Smoothing;Nonparametric Goodness-of-fit Test"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://scholarbank.nus.edu.sg/bitstreams/f58fea2d-f503-4465-9470-4ef6cb35a46b/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Nonparametric goodness-of-fit tests often result in test statistic which can be written as a random variable of chi-square-type mixtures. Zhang (2003) proposed to approximate its distribution using a random variable of form chi-square-type mixtures via matching the first three cumulants. In this thesis, we attempt to improve this approximation via matching the first four cumulants using a random variable of form non-central chi-square mixtures, resulting in the so-called non-central chi-square-approximation. Application of the results to nonparametric goodness-of-fit test based on local polynomial smoother is investigated. Two simulation studies are conducted to compare the non-central chi-square-approximation, the central chi-square-approximation and the normal approximation numerically. 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Application of the results to nonparametric goodness-of-fit test based on local polynomial smoother is investigated. Two simulation studies are conducted to compare the non-central chi-square-approximation, the central chi-square-approximation and the normal approximation numerically. The methodologies are illustrated using a real data example."],"dc:format.checksum.md5":["9754b1cb7e5711bcc03a6c42a2053c95","abaa7615ea318f5b9782aaffb5fcac02"],"dc:identifier.uri":["https://scholarbank.nus.edu.sg/bitstreams/f58fea2d-f503-4465-9470-4ef6cb35a46b/download"],"dc:relation.isreferencedby":["https://scholarbank.nus.edu.sg/handle/10635/14370"],"dc:subject":["x2-type mixtures;Local Polynomial Smoothing;Nonparametric Goodness-of-fit Test"],"dc:title":["Approximating the distributions of x2-type mixtures via matching four cumulants"],"dc:type":["Thesis"]},"updated_at":"2026-07-24T03:31:51Z"}