Return to search

Fractional principal components regression: a general approach to biased estimators

Several biased estimators have been proposed as alternatives to the least squares estimator when multicollinearity is present in the multiple linear regression model. Though the ridge estimator and the principal components estimator have been widely used for such problems, it should be noted that their performances in terms of mean square error are dependent upon the orientation of the unknown parameter vector and the magnitude of σ².

By defining the fractional principal components regression model as

y̲ = Zα̲ + 𝛜̲

= ZF⁻α<sub>F</sub> + 𝛜̲

where α<sub>F</sub> = Fα̲ and F⁻ is a generalized inverse of a diagonal matrix P, the resulting estimators of α̲<sub>F</sub>, based on various forms of F, are shown to define the class of the fractional principal components estimators. In the fractional principal components framework, several new estimation techniques are developed. The performances of the new estimators are evaluated and compared with other commonly used biased estimators both theoretically and by simulation studies. / Ph. D. / incomplete_metadata

Identiferoai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/49819
Date January 1986
CreatorsLee, Wonwoo
ContributorsStatistics, Birch, Jeffrey B., Myers, Raymond, Skarpness, Bradley O., Smith, Eric P., Hinkelmann, Klaus
PublisherVirginia Polytechnic Institute and State University
Source SetsVirginia Tech Theses and Dissertation
LanguageEnglish
Detected LanguageEnglish
TypeDissertation, Text
Formatix, 145 leaves, application/pdf, application/pdf
RightsIn Copyright, http://rightsstatements.org/vocab/InC/1.0/
RelationOCLC# 13830444

Page generated in 0.0016 seconds