Deletion of Principal Components in Regression.
SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
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Two techniques generally advocated for the deletion of principal components in regression analysis are delete components associated with small latent roots XX and delete components following nonrejection of a statistical test of the significance of the components. The estimator corresponding to the first procedure is referred to as a restricted least squares estimator and that associated with the second is called a preliminary test estimator. Properties of these estimators are examined in this paper with special attention to the effects of multicollinearities on the preliminary test estimator. The restricted estimator is recommended for use useless inferences on the noncentrality parameter of the preliminary test clearly indicate that the test will have adequate power.
- Statistics and Probability