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

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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Electrical and Computer Engineering

Department dc:contributor.department

Electrical and Computer Engineering

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2008

Author dc:creator

• D'Ambrosio, Philip

Chair dc:contributor.committeechair

• Mili, Lamine M.

Committee members dc:contributor.committeemember

• Wang, Yong
• Beex, A. A. Louis

• Minimum Hellinger Distance
• Power Systems
• Robust Estimation
• Information Geometry

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-05052008-124120

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/32228