{"id":{"repo_id":"ksu","oai_identifier":"oai:krex.k-state.edu:2097/17338"},"canonical_url":"https://search.dev.ndltd.org/etd/ksu/oai:krex.k-state.edu:2097/17338","repository":{"repo_id":"ksu","name":"Kansas State University","base_url":"https://krex.k-state.edu/server/oai/request"},"display":{"title":"Semiparametric mixture models","abstract":"This dissertation consists of three parts that are related to semiparametric mixture models. In Part I, we construct the minimum profile Hellinger distance (MPHD) estimator for a class of semiparametric mixture models where one component has known distribution with possibly unknown parameters while the other component density and the mixing proportion are unknown. Such semiparametric mixture models have been often used in biology and the sequential clustering algorithm. In Part II, we propose a new class of semiparametric mixture of regression models, where the mixing proportions and variances are constants, but the component regression functions are smooth functions of a covariate. A one-step backfitting estimate and two EM-type algorithms have been proposed to achieve the optimal convergence rate for both the global parameters and nonparametric regression functions. We derive the asymptotic property of the proposed estimates and show that both proposed EM-type algorithms preserve the asymptotic ascent property. In Part III, we apply the idea of single-index model to the mixture of regression models and propose three new classes of models: the mixture of single-index models (MSIM), the mixture of regression models with varying single-index proportions (MRSIP), and the mixture of regression models with varying single-index proportions and variances (MRSIPV). Backfitting estimates and the corresponding algorithms have been proposed for the new models to achieve the optimal convergence rate for both the parameters and the nonparametric functions. We show that the nonparametric functions can be estimated as if the parameters were known and the parameters can be estimated with the same rate of convergence, n[subscript](-1/2), that is achieved in a parametric model.","abstract_html":"This dissertation consists of three parts that are related to semiparametric mixture models. In Part I, we construct the minimum profile Hellinger distance (MPHD) estimator for a class of semiparametric mixture models where one component has known distribution with possibly unknown parameters while the other component density and the mixing proportion are unknown. Such semiparametric mixture models have been often used in biology and the sequential clustering algorithm. In Part II, we propose a new class of semiparametric mixture of regression models, where the mixing proportions and variances are constants, but the component regression functions are smooth functions of a covariate. A one-step backfitting estimate and two EM-type algorithms have been proposed to achieve the optimal convergence rate for both the global parameters and nonparametric regression functions. We derive the asymptotic property of the proposed estimates and show that both proposed EM-type algorithms preserve the asymptotic ascent property. In Part III, we apply the idea of single-index model to the mixture of regression models and propose three new classes of models: the mixture of single-index models (MSIM), the mixture of regression models with varying single-index proportions (MRSIP), and the mixture of regression models with varying single-index proportions and variances (MRSIPV). Backfitting estimates and the corresponding algorithms have been proposed for the new models to achieve the optimal convergence rate for both the parameters and the nonparametric functions. We show that the nonparametric functions can be estimated as if the parameters were known and the parameters can be estimated with the same rate of convergence, n[subscript](-1/2), that is achieved in a parametric model.","abstract_has_math":false,"creators":["Xiang, Sijia"],"institution":"Kansas State University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-04-21","date_published":"2014-04-21","updated_at":"2026-07-27T20:01:24Z","subjects":["Semiparametric mixture models","Kernel regression","EM algorithm"],"languages":["en_US"],"rights":["© the author. This Item is protected by copyright and/or related rights. 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This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s)."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/2097/17338"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This dissertation consists of three parts that are related to semiparametric mixture models. In Part I, we construct the minimum profile Hellinger distance (MPHD) estimator for a class of semiparametric mixture models where one component has known distribution with possibly unknown parameters while the other component density and the mixing proportion are unknown. Such semiparametric mixture models have been often used in biology and the sequential clustering algorithm. In Part II, we propose a new class of semiparametric mixture of regression models, where the mixing proportions and variances are constants, but the component regression functions are smooth functions of a covariate. A one-step backfitting estimate and two EM-type algorithms have been proposed to achieve the optimal convergence rate for both the global parameters and nonparametric regression functions. We derive the asymptotic property of the proposed estimates and show that both proposed EM-type algorithms preserve the asymptotic ascent property. In Part III, we apply the idea of single-index model to the mixture of regression models and propose three new classes of models: the mixture of single-index models (MSIM), the mixture of regression models with varying single-index proportions (MRSIP), and the mixture of regression models with varying single-index proportions and variances (MRSIPV). Backfitting estimates and the corresponding algorithms have been proposed for the new models to achieve the optimal convergence rate for both the parameters and the nonparametric functions. We show that the nonparametric functions can be estimated as if the parameters were known and the parameters can be estimated with the same rate of convergence, n[subscript](-1/2), that is achieved in a parametric model."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Doctor of Philosophy"]},{"key":"dc:title","label":"Title","values":["Semiparametric mixture models"]}]}],"canonical_facts":{"dc:creator":["Xiang, Sijia"],"dc:date.accessioned":["2014-04-21T14:15:25Z"],"dc:date.available":["2014-04-21T14:15:25Z"],"dc:date.issued":["2014-04-21"],"dc:description.abstract":["This dissertation consists of three parts that are related to semiparametric mixture models. In Part I, we construct the minimum profile Hellinger distance (MPHD) estimator for a class of semiparametric mixture models where one component has known distribution with possibly unknown parameters while the other component density and the mixing proportion are unknown. Such semiparametric mixture models have been often used in biology and the sequential clustering algorithm. In Part II, we propose a new class of semiparametric mixture of regression models, where the mixing proportions and variances are constants, but the component regression functions are smooth functions of a covariate. A one-step backfitting estimate and two EM-type algorithms have been proposed to achieve the optimal convergence rate for both the global parameters and nonparametric regression functions. We derive the asymptotic property of the proposed estimates and show that both proposed EM-type algorithms preserve the asymptotic ascent property. In Part III, we apply the idea of single-index model to the mixture of regression models and propose three new classes of models: the mixture of single-index models (MSIM), the mixture of regression models with varying single-index proportions (MRSIP), and the mixture of regression models with varying single-index proportions and variances (MRSIPV). Backfitting estimates and the corresponding algorithms have been proposed for the new models to achieve the optimal convergence rate for both the parameters and the nonparametric functions. We show that the nonparametric functions can be estimated as if the parameters were known and the parameters can be estimated with the same rate of convergence, n[subscript](-1/2), that is achieved in a parametric model."],"dc:description.degree":["Doctor of Philosophy"],"dc:identifier.uri":["http://hdl.handle.net/2097/17338"],"dc:language.iso":["en_US"],"dc:publisher":["Kansas State University"],"dc:rights":["© the author. This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s)."],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Semiparametric mixture models","Kernel regression","EM algorithm"],"dc:title":["Semiparametric mixture models"],"dc:type":["Dissertation"]},"updated_at":"2026-07-27T20:01:24Z"}