Finite Population Optimal Prediction

In this paper, we consider the linear model.y = Xβ + eWhere e is a n × 1 random error vector with E(e) = 0 and Cov(e) = σ2V,σ2 >0 is unknown parameter but V>0 is known matrix, β isunknown p - dimensional parameter.First, in this paper, we study the simple projection predictor of the model. The optimal prediction condition of SPP is given and the robustness of the SPP on the covariance matrix is investigated.Second, we study the linear Minimax predictor of the model under the supposed condition: V > 0. Choosing quadratic loss function, we have the uniquelinear Minimax predictor of Ay in Ω.Last, In connection with the abnormal state of X, we give the generalized compressed predictor of the model under the supposed condition: V = IN and2 <, rankX = p <, N . In connection with the Prediction Mean, the generalizedcompressed predictor isn't as good as the other.