A Differential Geometry-Based Algorithm for Solving the Minimum Hellinger Distance Estimator

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dc.contributor.authorD'Ambrosio, Philipen
dc.contributor.committeechairMili, Lamine M.en
dc.contributor.committeememberWang, Yongen
dc.contributor.committeememberBeex, A. A. Louisen
dc.contributor.departmentElectrical and Computer Engineeringen
dc.date.accessioned2014-03-14T20:35:08Zen
dc.date.adate2008-05-28en
dc.date.available2014-03-14T20:35:08Zen
dc.date.issued2008-04-21en
dc.date.rdate2008-05-28en
dc.date.sdate2008-05-05en
dc.description.abstractRobust 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.en
dc.description.degreeMaster of Scienceen
dc.identifier.otheretd-05052008-124120en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-05052008-124120/en
dc.identifier.urihttp://hdl.handle.net/10919/32228en
dc.publisherVirginia Techen
dc.relation.haspartREVISED_FINAL_DAmbrosio_MS_Thesis_27_May_2008b.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectMinimum Hellinger Distanceen
dc.subjectPower Systemsen
dc.subjectRobust Estimationen
dc.subjectInformation Geometryen
dc.titleA Differential Geometry-Based Algorithm for Solving the Minimum Hellinger Distance Estimatoren
dc.typeThesisen
thesis.degree.disciplineElectrical and Computer Engineeringen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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