Ill-conditioned information matrices and the generalized linear model: an asymptotically biased estimation approach

In the regression framework of the generalized linear model (Nelder and Wedderburn (1972)), interative maximum likelihood parameter estimation is employed via the method of scoring. This iterative procedure involves a key matrix, the information matrix. Ill-conditioning of the information matrix can be responsible for making many desirable properties of the parameter estimates unattainable. Some asymptotically biased alternatives to maximum likelihood estimation are put forth which alleviate the detrimental effects of near singular information. Notions of ridge estimation (Hoerl and Kennard (1970a) and Schaefer (1979)), principal component estimation (Webster et al. (1974) and Schaefer (1986)), and Stein estimation (Stein (1960)) are extended into a regression setting utilizing any one of an entire class of response distributions.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Statistics

Department dc:contributor.department

Statistics

Grantor dc:publisher

Virginia Polytechnic Institute and State University

Year dc:date.issued

1988

Author dc:creator

• Marx, Brian D.

Chairs dc:contributor.committeechair

• Smith, Eric P.
• Hinkelmann, Klaus

Committee members dc:contributor.committeemember

• Myers, Raymond
• Birch, Jeffrey B.
• Terrell, George R.
• Brooks, Camilla A.

Statement dc:rights

• In Copyright

Licence dc:rights.uri

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

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/10919/53584

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/53584