Principal Component Estimation for Generalized Linear Regression
针对广义线性回归，提出一种有渐近偏差的主成分参数估计方法，作为传统最大似然估计的替代，尤其适用于信息矩阵病态的情况，并量化了偏差、方差和均方误差。
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.