Principal component estimation for generalized linear regression

SUMMARY The generalized linear model (Nelder & Wedderburn, 1972) has become an elegant and practical option to classical least-squares linear model building. We consider the specific problem of generalized linear regression utilizing a set of continuous explanatory variables to model an exponential family response. It is the objective of this paper to develop and present an asymptotically biased principal component parameter estimation technique, as an option to traditional maximum likelihood estimation for generalized linear regression. Both iterative and one-step principal component estimators are developed, directly compared, and can be particularly useful with the presence of an ill-conditioned information matrix. The bias, variance and mean squared error of principal component estimation will be quantified. Generalizations for rules of deletion of components will be examined. Lastly, an example employs principal component estimation for Poisson response data.