Bias Predictors In The Finite Populations In Linear Model

In the linear model,one of the most important research fields is prediction.The prediction is to use present data to predict the future value.Researchers obtain the best unbiased linear predictors of(?)_BUPas well as(?)_SPP=l'_n X(?)_s and (?)_BUP=l'y on each kind of linear model such as general Gauss-Markov model, multivariate linear models,growth curve model and so on.Furthermore,the systematic and complete theory results have been obtained.Also,Wang Songgui proposes an auto-adapted ridge prediction ofθ=l'y in the finite populations which is the beginning of domestic bias prediction researching.In this paper,we first describe the research of prediction in the finite population.In the chapter 2,we state some basic theory of matrix,linear model and prediction.And then,in the chapter 3,we introduce some conclusions about the auto-adapted ridge predictor which can be used to obtain the generalized ridge predictor which is proved dominate the best linear unbiased prediction under PMSE.Moreover,the generalized ridge prediction is the admissible prediction under the matrix loss and is the Minimax prediction under the square loss.At the end of this chapter,we use the real data as the example to prove the generalized ridge prediction superiors to the best linear unbiased prediction.In the chapter 4,we respect discuss the generalized ridge principal components estimator and LIU-estimator,obtain the generalized ridge principal component prediction and LIU-prediction,and prove some of theirs properties such as the admissibility and the Minimax predictions.