{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/32228"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/32228","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"A Differential Geometry-Based Algorithm for Solving the Minimum Hellinger Distance Estimator","abstract":"Robust estimation of statistical parameters is traditionally believed to exist in a trade space between robustness and efficiency. This thesis examines the Minimum Hellinger Distance Estimator (MHDE), which is known to have desirable robustness properties as well as desirable efficiency properties. This thesis confirms that the MHDE is simultaneously robust against outliers and asymptotically efficient in the univariate location case. Robustness results are then extended to the case of simple linear regression, where the MHDE is shown empirically to have a breakdown point of 50%. A geometric algorithm for solution of the MHDE is developed and implemented. The algorithm utilizes the Riemannian manifold properties of the statistical model to achieve an algorithmic speedup. The MHDE is then applied to an illustrative problem in power system state estimation. The power system is modeled as a structured linear regression problem via a linearized direct current model; robustness results in this context have been investigated and future research areas have been identified from both a statistical perspective as well as an algorithm design standpoint.","abstract_html":"Robust estimation of statistical parameters is traditionally believed to exist in a trade space between robustness and efficiency. This thesis examines the Minimum Hellinger Distance Estimator (MHDE), which is known to have desirable robustness properties as well as desirable efficiency properties. This thesis confirms that the MHDE is simultaneously robust against outliers and asymptotically efficient in the univariate location case. Robustness results are then extended to the case of simple linear regression, where the MHDE is shown empirically to have a breakdown point of 50%. A geometric algorithm for solution of the MHDE is developed and implemented. The algorithm utilizes the Riemannian manifold properties of the statistical model to achieve an algorithmic speedup. The MHDE is then applied to an illustrative problem in power system state estimation. The power system is modeled as a structured linear regression problem via a linearized direct current model; robustness results in this context have been investigated and future research areas have been identified from both a statistical perspective as well as an algorithm design standpoint.","abstract_has_math":false,"creators":["D'Ambrosio, Philip"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Electrical and Computer Engineering","degree_department":"Electrical and Computer Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":["Mili, Lamine M."],"committee_members":["Wang, Yong","Beex, A. A. Louis"],"year":2008,"date_issued":"2008-04-21","date_published":"2008-04-21","updated_at":"2026-07-22T22:19:24Z","subjects":["Minimum Hellinger Distance","Power Systems","Robust Estimation","Information Geometry"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-05052008-124120"],"render_values":[{"text":"etd-05052008-124120","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/32228","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Mili, Lamine M."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Wang, Yong","Beex, A. A. Louis"]},{"key":"dc:contributor.department","label":"Department","values":["Electrical and Computer Engineering"]},{"key":"dc:creator","label":"Author","values":["D'Ambrosio, Philip"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T20:35:08Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T20:35:08Z","2008-05-28"]},{"key":"dc:date.issued","label":"Date","values":["2008-04-21"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical and Computer Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Minimum Hellinger Distance","Power Systems","Robust Estimation","Information Geometry"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-05052008-124120"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/32228"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Robust estimation of statistical parameters is traditionally believed to exist in a trade space between robustness and efficiency. This thesis examines the Minimum Hellinger Distance Estimator (MHDE), which is known to have desirable robustness properties as well as desirable efficiency properties. This thesis confirms that the MHDE is simultaneously robust against outliers and asymptotically efficient in the univariate location case. Robustness results are then extended to the case of simple linear regression, where the MHDE is shown empirically to have a breakdown point of 50%. A geometric algorithm for solution of the MHDE is developed and implemented. The algorithm utilizes the Riemannian manifold properties of the statistical model to achieve an algorithmic speedup. The MHDE is then applied to an illustrative problem in power system state estimation. The power system is modeled as a structured linear regression problem via a linearized direct current model; robustness results in this context have been investigated and future research areas have been identified from both a statistical perspective as well as an algorithm design standpoint."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["A Differential Geometry-Based Algorithm for Solving the Minimum Hellinger Distance Estimator"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Mili, Lamine M."],"dc:contributor.committeemember":["Wang, Yong","Beex, A. A. Louis"],"dc:contributor.department":["Electrical and Computer Engineering"],"dc:creator":["D'Ambrosio, Philip"],"dc:date.accessioned":["2014-03-14T20:35:08Z"],"dc:date.available":["2014-03-14T20:35:08Z","2008-05-28"],"dc:date.issued":["2008-04-21"],"dc:description.abstract":["Robust estimation of statistical parameters is traditionally believed to exist in a trade space between robustness and efficiency. This thesis examines the Minimum Hellinger Distance Estimator (MHDE), which is known to have desirable robustness properties as well as desirable efficiency properties. This thesis confirms that the MHDE is simultaneously robust against outliers and asymptotically efficient in the univariate location case. Robustness results are then extended to the case of simple linear regression, where the MHDE is shown empirically to have a breakdown point of 50%. A geometric algorithm for solution of the MHDE is developed and implemented. The algorithm utilizes the Riemannian manifold properties of the statistical model to achieve an algorithmic speedup. The MHDE is then applied to an illustrative problem in power system state estimation. The power system is modeled as a structured linear regression problem via a linearized direct current model; robustness results in this context have been investigated and future research areas have been identified from both a statistical perspective as well as an algorithm design standpoint."],"dc:description.degree":["Master of Science"],"dc:identifier.other":["etd-05052008-124120"],"dc:identifier.uri":["http://hdl.handle.net/10919/32228"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Minimum Hellinger Distance","Power Systems","Robust Estimation","Information Geometry"],"dc:title":["A Differential Geometry-Based Algorithm for Solving the Minimum Hellinger Distance Estimator"],"dc:type":["Thesis"],"thesis:degree_discipline":["Electrical and Computer Engineering"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:24Z"}