Biased Estimation in Regression

Abstract
Important theoretical advances were obtained for the latent root, principal component, and ridge estimators of the parameters of multiple linear regression models. Specifically, theoretical comparisons among these estimators and the classical least squares estimator revealed that the biased estimators offer great potential for more accurate estimation than least squares when predictor variables are multicollinear. Among the biased estimators, all three compete favorably over a wide range of model configurations with each being able to estimate more accurately than the others for certain types of model configurations. Special emphasis has been directed toward the investigation of the latent root regression estimator. Its theoretical efficacy and asymptotic properties have been developed and its potential for improvement over other biased estimators has been shown. (KR)

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