Considering the generalized linear regression model and its prediction problem of biased estimation,this paper discusses its superiority of the optimal and classical predictors based on the shrunken principal estimator by criteria of mean dispersion error matrix and generalized risk function.

The paper discusses some characteristics of the shrunken principal estimator,proves that the shrunhen principal estimate is better than LS estimator under GMSE and Pitman抯 Measure of Clossness and makes some additions to Y抯 prediction characteristic

The paper discusses some characteristics of the shrunken principal estimator and proves that the shrunhen principal estimate is better than LS estimator under GMSM and Pitman’s Measure of Clossness.

This paper considers the classification compression principal component estimate of regression coefficient in growth curve model and proves that it is superior to least squares estimate.

In this paper it is proved that under Pitman Closeness criterion the principal components estimate is superior to the generalized LSE of parameters in variance component model, with the distribution of the random effect vectors being normal.

Principal Components Estimate of Regression Coefficient of Multivariate Linear Regression Model;

The paper propounds two new estimates,which are named BL estimate(Bayesian estimate combined with Latent root estimate)and BP estimate(Bayesian estimate combined with Principal components estimate).

We generalized the ridge combined component estimation and (k) is the generalized ridge combined principal component estimation.